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Professors Friedman, Hunter†, Hall, Jagannathan‡, and Loinaz (Chair); Assistant Professors Carter and Hanneke.

†On leave fall semester 2015-16. ‡On leave spring semester 2015-16.

The Departments of Physics and Astronomy were combined into a new Department of Physics and Astronomy beginning in the 2014-15 academic year.

Physics

Physics is the study of the natural world emphasizing an understanding of phenomena in terms of fundamental interactions and basic laws. As such, physics underlies all of the natural sciences and pervades contemporary approaches to the study of the universe (astronomy and astrophysics), living systems (biophysics and neuroscience), chemistry (chemical physics), and earth systems (geophysics and environmental science). In addition, the relationship of physics to mathematics is deep, complex and rich. To reflect the broad range of activities pursued by people with training in physics, the department has developed a curriculum that provides a solid background in the fundamentals of physics while allowing some flexibility, particularly at the upper level, for students’ interests in astronomy, biology, chemistry, computer science, geology, mathematics and neuroscience.

The core physics program provides a course of study for those who are interested in physics as a liberal arts major, with career plans in diverse fields such as law, medicine, business and education. The department also provides a number of upper-level electives to deepen the background of those students intending to pursue careers in physics and closely related technical fields.

The sequence PHYS 116, 117 may be taken by students who require two semesters of physics with laboratory. MATH 111 is a requisite for PHYS 116. There is no additional mathematics requirement for PHYS 117. Students interested in majoring in physics should take PHYS 123 and 124 early in their college career. Those who have taken PHYS 116 and 117 are also able to join the majors’ stream, but they should discuss the transition with a faculty member as early as they can. The general content of the two sequences is similar, but the mathematical levels are different. MATH 121 is a requisite for PHYS 124, but not for PHYS 117. Hence, students who wish to major after completing PHYS 117 should complete MATH 121.

*Major Program. *Students who wish to major in physics are required to take MATH 111 and 121, and PHYS 123, 124 (or PHYS 116, 117, but see above), 225, 226, 227, 230 (or CHEM 361), 343, 347 and 348. Students may petition the Department to substitute an upper-level course in a related discipline for a required upper level departmental course. Students planning a career in physics should seriously consider taking one or more electives in physics and mathematics. PHYS 452 is an advanced course in electromagnetic theory and will follow the required intermediate course on the subject, PHYS 347; similarly, PHYS 453, an advanced course in quantum mechanics, will follow PHYS 348. PHYS 460 is a course on General Relativity. Not all these electives may be offered every year, and from time to time, the department may offer other upper-level electives.

All Physics majors must demonstrate satisfactory performance on an approved standardized test in general physics prior to the beginning of the second semester of the senior year. Students failing to do so must instead pass an alternate comprehensive examination in the second semester of the senior year. All Physics majors must also attend at least nine public physics lectures during the senior year.

*General Education Physics Courses*. The Physics Department offers a variety of courses for students not majoring in the sciences. Typically these courses do not assume any background beyond high-school mathematics. In most years, the department teaches a few of these courses.

*Departmental Honors Program. *Students who wish to receive departmental Honors should enroll in PHYS 498 and 499D in addition to completing the other requirements for the major. To enter the Honors program, a student must attain an average grade of at least B- in all Physics courses taken through the end of the junior year or receive department approval. At the end of the first semester of the senior year the student’s progress on the Honors problem will determine the advisability of continuation in the Honors program.

The aim of Departmental Honors work in Physics is to provide the student an opportunity to pursue, under faculty direction, in-depth research into a project in experimental and/or theoretical physics. Current experimental areas of research in the department include atomic and molecular physics, precision measurements and fundamental symmetries, Bose-Einstein condensation, ultracold collisions, the quantum-classical frontier, nonlinear dynamics, optical trapping, ion trapping, cellular and molecular mechanics, and phase transitions. Theoretical work is primarily in the area of High Energy and Elementary Particle physics, but faculty members pursue studies in quantum computers, foundations of quantum mechanics, and classical gravitation theory. In addition to apparatus for projects closely related to the continuing experimental research activity of faculty members, facilities are available for experimental projects in many other areas. Subject to availability of equipment and faculty interest, Honors projects arising out of students’ particular interests are encouraged. Students must submit a written thesis on the Honors work a few weeks before the end of their final semester (in late April for spring graduation). Students give a preliminary presentation of their work during the first semester, and a final presentation at the end of the second semester. In addition, they take oral examinations devoted primarily to the thesis work. The departmental recommendation for the various levels of Honors will be based on the student’s record, Departmental Honors work, Comprehensive Examination and oral examination on the thesis.

Astronomy

Astronomy was the first science, and it remains one of the most exciting and active fields of scientific research. Opportunities exist to pursue studies both at the non-technical and advanced levels. Non-technical courses are designed to be accessible to every Amherst student: their goal is to introduce students to the roles of quantitative reasoning and observational evidence, and to give some idea of the nature of the astronomical universe. These courses are often interdisciplinary in nature, including discussion of issues pertaining to Earth Sciences and Physics. Advanced students pursue a study of Physics, Mathematics, Computer Science, as well as Astronomy.

A joint Five College Astronomy Department provides instruction at Amherst, Hampshire, Mount Holyoke and Smith Colleges and the University of Massachusetts (http://www.astro.umass.edu/about/fcad/). All introductory courses and some advanced courses are taught at Amherst, but students are also encouraged to take advanced courses at the four other institutions. As a result of this partnership, students can enjoy the benefits of a first-rate liberal arts education while maintaining association with a research department of international stature. Students may pursue independent theoretical and observational work in association with Amherst Professors Haggard and Cowan, or with any member of the Five College Astronomy Department, either during the academic year or the summer term. The notation “FC” indicates courses offered by the Five College Astronomy Department. The facilities of all five institutions are available to departmental majors.

*Major Program.* The Astronomy major consists of nine required courses (MATH 111, MATH 121, STAT 135, PHYS 123 (or 116), PHYS 124 (or 117), COSC 111, ASTR 228, ASTR 335, and ASTR 352, and three electives from the list below. Those who have taken PHYS 116 and 117 are also able to join the majors’ stream, but they should discuss the transition with a faculty member as early as they can. In addition, all Astronomy majors must pass a written comprehensive examination in the second semester of their senior year. Astronomy majors must also attend at least nine public astronomy lectures during the senior year.

Of the three elective courses, at least one elective must be in Astronomy, at least two must be 300-level or higher. Elective courses not on this list may count toward the major with departmental approval. These electives include: ASTR 220, 223, 224, 225, 226, 330, 337, and 341; CHEM 351 and 361; GEOL 341 and 431; MATH 230, 335, and 360; PHYS 230, 343, and 347; COSC 201, 301, and 341.

*Departmental Honors Program.* Students who wish to receive departmental Honors should enroll in ASTR 498 and 499 in addition to completing the other requirements for the major. To enter the Honors program, a student must attain an average grade of at least B– in all required courses taken through the end of the junior year or receive department approval. At the end of the first semester of the senior year the student’s progress on the Honors problem will determine the advisability of continuation in the Honors program.

The aim of Departmental Honors work in Astronomy is to provide the student an opportunity to pursue, under faculty direction, in-depth research into a project in observational and/or theoretical astronomy. Current areas of research at Amherst include active galactic nuclei (accreting supermassive black holes) and their host galaxies, the Galactic Center and Sgr A*, accretion-driven outflows, multi-wavelength and time domain surveys, high-precision infrared photometry, atmospheric characterization of extrasolar planets, and the modeling of planetary climate. Additional opportunities within the Five College Astronomy Department include cosmology, cosmogony, radio astronomy, relativistic astrophysics, laboratory astrophysics, gravitational theory, infrared balloon astronomy, stellar astrophysics, spectroscopy, and exobiology. Facilities include the Five College Radio Astronomy Observatory, the Laboratory for Infrared Astrophysics, the Large Millimeter Telescope, balloon astronomy equipment (16-inch telescope, cryogenic detectors), and modern 24- and 16-inch Cassegrain reflectors. Subject to availability of resources and faculty interest, Honors projects arising out of students’ particular interests are encouraged.

Students must submit a written thesis on the Honors work a few weeks before the end of their final semester (in late April for spring graduation). Students give a preliminary presentation of their work during the first semester, and a final presentation at the end of the second semester. In addition, they take oral examinations devoted primarily to the thesis work. The departmental recommendation for the various levels of Honors will be based on the student’s record, Departmental Honors work, Comprehensive Examination, and Oral Examination on the thesis.

*General Education Astronomy Courses. *The Astronomy Department offers a variety of courses for students not majoring in Astronomy. These include ASTR 111 and 112.

Students may search for Astronomy courses through the Five College online catalog. The Website is http://www.astro.umass.edu/academics/courses/

An introduction to the cosmos, with an emphasis on modern theories and observations. We'll discuss the nature and evolution of stars, our Milky Way Galaxy, external galaxies, black holes, and the origin and fate of the universe itself. The emphasis will be on conceptual, as contrasted with mathematical, comprehension, making this an excellent opportunity for non-science majors. Two 80-minute sessions per week.

Not open to upper-division students majoring in the physical sciences. Fall semester. Professor TBA.

Thousands of planets have been discovered since the 1990s, all of them orbiting other stars. The existence of extrasolar planets confirms that planets are commonplace, but closer inspection of these planetary systems reveals that they are completely different from our Solar System. We will discuss how planets form, how they change with time, and how we can observe them with current and planned telescopes. Along the way, students will explore what makes Earth habitable and will estimate the likelihood that such conditions exist on nearby exoplanets. Two 80-minute sessions per week.

Not open to upper-division students majoring in the physical sciences. Omitted 2015-16. Professor TBA.

Black holes, agglomerations of mass so dense that even light cannot escape their gravitational pull, are among the simplest and yet most exotic objects in astrophysics. Some black holes are the fossils of supernovae, exploding stars that leave behind a remnant with a mass tens or hundreds of times the mass of our sun. Other "supermassive" black holes lurk at the hearts of galaxies, including our Milky Way. These monsters (sometimes a billion times the mass of our sun) have a profound impact on the formation and structure of their host galaxies, despite being packed into structures smaller than the solar system. In this course, we will explore the astrophysical evidence for black holes, the basic theory required to begin to understand them, and the many active research questions surrounding their origins and their impacts on our physical universe.

Requisite: MATH 111 and PHYS 123 or 116, concurrent enrollment acceptable. Omitted 2015-16.

Cosmological models and the relationship between models and observable parameters. Topics in current astronomy that bear upon cosmological problems, including background electromagnetic radiation, nucleosynthesis, dating methods, determinations of the mean density of the universe and the Hubble constant, and tests of gravitational theories. Discussion of questions concerning the foundations of cosmology and its future as a science.

Requisites: MATH 111 and one course in the physical sciences. Spring semester. Professor TBA.

A calculus-based introduction to the properties, structure, formation and evolution of stars and galaxies. The laws of gravity, thermal physics, and atomic physics provide a basis for understanding observed properties of stars, interstellar gas and dust. We apply these concepts to develop an understanding of stellar atmospheres, interiors, and evolution, the interstellar medium, and the Milky Way and other galaxies.

Requisite: MATH 121 and PHYS 124 or 117, concurrent enrollment acceptable. Spring semester. Professor TBA.

The same basic laws describe stars and planets. We will learn about equations of state as well as radiative and convective heat transport in order to understand the steady-state structure of stellar and planetary interiors and atmospheres. We will then see how waves propagate through these bodies, producing stellar pulsations, earthquakes, and weather.

Requisite: MATH 121 and PHYS 124 or 117. Fall semester. Professor TBA.

In this course we provide an introduction to the techniques of gathering and analyzing ground- and space-based astronomical data at multiple wavelengths (X-ray, optical, infrared, and radio). The course will cover methods for astronomical data acquisition and analysis using the Python computing language. Topics covered include: astronomical coordinate and time systems; telescope design and optics; instrumentation and techniques for imaging, photometry, and spectroscopy; astronomical detectors; digital image processing tools and techniques; atmospheric phenomena affecting astronomical observations; and error analysis and curve fitting.

Requisites: At least one of ASTR 224, 225, 226, 228 or 335. Previous experience in computer programming is strongly recommended. Fall semester. Professor TBA.

Independent Reading Course.

Fall and spring semesters. The Department.

Opportunities for theoretical and observational work on the frontiers of science are available in cosmology, cosmogony, radio astronomy, planetary atmospheres, relativistic astrophysics, laboratory astrophysics, gravitational theory, infrared balloon astronomy, stellar astrophysics, spectroscopy, and exobiology. Facilities include the Five College Radio Astronomy Observatory, the Laboratory for Infrared Astrophysics, balloon astronomy equipment (16-inch telescope, cryogenic detectors), and modern 24- and 16-inch Cassegrain reflectors. An Honors candidate must submit an acceptable thesis and pass an oral examination. The oral examination will consider the subject matter of the thesis and other areas of astronomy specifically discussed in Astronomy courses.

Open to seniors. Required of Honors students. Spring semester. The Department.

We will develop the concept of energy from a Physics perspective. We will introduce the various forms that energy can take and discuss the mechanisms by which it can be generated, transmitted, and transformed. The law of conservation of energy will be introduced both as a useful tool, and as an example of a fundamental physical law. The environmental and financial costs and benefits of various methods of energy generation and consumption will be discussed. Demonstrations and hands-on laboratory experiences will be an integral part of the course. The course is intended for non-science majors and not for students who have either completed or intend to complete the equivalent of PHYS 117 or CHEM 110.

Requisite: A working knowledge of high-school algebra, geometry and trigonometry. Limited to 20 students. Spring semester. Professor Hunter.

This course will discuss Einstein's Special Theory of Relativity in quantitative detail, beginning with the roots of the principle of relativity in the writings of Galileo and Newton. We will then examine a qualitative outline of general relativity. We will next study the structure of matter and forces on the small scale and the challenges posed by the quantum theory, which provides the best description of the microworld. The last topic of the semester will be the application of relativity and quantum physics to the early universe. The course is designed for the non-specialist audience and will take an elementary but rigorous approach. No advanced mathematics or prior physics will be required; high school algebra and geometry will, however, be used extensively in class and in the problem sets. The work will require readings and regular problem sets, and students will also write a few essays.

Omitted 2015-16. Professor Jagannathan.

The course will begin with a description of the motion of particles and introduce Newton’s dynamical laws and a number of important force laws. We will apply these laws to a wide range of problems to gain a better understanding of the laws and to demonstrate the generality of the framework. The important concepts of work, mechanical energy, and linear and angular momentum will be introduced and the unifying idea of conservation laws will be discussed. The study of mechanical waves permits a natural transition from the dynamics of particles to the dynamics of waves, including the interference of waves. Additional topics may include fluid mechanics and rotational dynamics. Three hours of lecture. Also one three-hour laboratory per week.

Requisite: MATH 111. Limited to 48 students. Fall semester: Professor Friedman. Spring semester: Professor TBA.

Most of the physical phenomena we encounter in everyday life are due to the electromagnetic force. This course will begin with Coulomb’s law for the force between two charges at rest and introduce the electric field in this context. We will then discuss moving charges and the magnetic interaction between electric currents. The mathematical formulation of the basic laws in terms of the electric and magnetic fields will allow us to work towards the unified formulation originally given by Maxwell. His achievement has, as a gratifying outcome, the description of light as an electromagnetic wave. The course will consider both ray-optics and wave-optics descriptions of light. Laboratory exercises will emphasize electrical circuits, electronic measuring instruments, optics and optical experiments. Three hours of lecture and discussion and one three-hour laboratory per week.

Requisite: PHYS 116 or 123. Limited to 48 students. Fall semester: Professor Carter. Spring semester: Professors Carter and Loinaz.

Our everyday intuitions about physics completely break down when thinking about life at the nanoscale. At this scale, biological molecules are large and Brownian motion and viscous friction dominate. Yet, to design the next generation of medical technologies, including nanobots that augment the immune system or destroy cancer cells, we need to understand the physics at this scale. In this course, we will learn about the physics behind random molecular motion and how to create nanoscale-directed movement using an engine. We will learn about how to build a microscope to visualize a nanomachine and the physical properties of polymers that might be useful as building materials. By the end of the course, students will have a working knowledge of physics at the molecular scale, important in nanotechnology and drug design. Three hours of lecture and three hours of laboratory per week; the laboratory projects will require additional time outside of class hours.

Requisite: PHYS 116. Limited to 20 students. Omitted 2015-16. Professor Carter.

The idea that the same simple physical laws apply equally well in the terrestrial and celestial realms, called the Newtonian Synthesis, is a major intellectual development of the seventeenth century. It continues to be of vital importance in contemporary physics. In this course, we will explore the implications of this synthesis by combining Newton’s dynamical laws with his Law of Universal Gravitation. We will solve a wide range of problems of motion by introducing a small number of additional forces. The concepts of work, kinetic energy, and potential energy will then be introduced. Conservation laws of momentum, energy, and angular momentum will be discussed, both as results following from the dynamical laws under restricted conditions and as general principles that go well beyond the original context of their deduction. Newton’s laws will be applied to a simple continuous medium to obtain a wave equation as an approximation. Properties of mechanical waves will be discussed. Four hours of lecture and discussion and one three-hour laboratory per week.

Requisite: MATH 111. Limited to 24 students. Fall semester. Professor Hanneke.

In the mid-nineteenth century, completing nearly a century of work by others, Maxwell developed an elegant set of equations describing the dynamical behavior of electromagnetic fields. A remarkable consequence of Maxwell’s equations is that the wave theory of light is subsumed under electrodynamics. Moreover, we know from subsequent developments that the electromagnetic interaction largely determines the structure and properties of ordinary matter. The course will begin with Coulomb’s Law but will quickly introduce the concept of the electric field. Students will explore moving charges and their connection with the magnetic field, study currents and electrical circuits, and discuss Faraday’s introduction of the dynamics of the magnetic field and Maxwell’s generalization. Laboratory exercises will concentrate on circuits, electronic measuring instruments, and optics. Four hours of lecture and discussion and one three-hour laboratory per week.

Requisite: MATH 121 and PHYS 116 or 123. Limited to 24 students. Spring semester. Professor TBA.

This course is designed for math and science students who are not majoring in physics but would like to learn the principles of quantum mechanics rigorously. For the most part, we will discuss the so-called two-level systems and collections of such systems. A two-level system has two basic states from which all other states may be constructed by linear combinations. We will begin with a review of linear algebra in two dimensions where the normalized vectors represent physical states and 2 x 2 matrices represent physical quantities and transformations. We will introduce the algebra of complex numbers as needed. Our prime examples will be an electron spin in an external field, and the various polarization states of the photon. Next we will consider a larger system that consists of several two-level subsystems. Though such a system is still very simple to describe, surprisingly, it exhibits nearly all the subtle and challenging features of the quantum theory. With the formalism developed, we will explore a range of foundational questions and applications such as uncertainty and measurement, entanglement, the EPR challenge and Bell’s theorem, the no-cloning theorem and teleportation. The work in the course comprises regular problem sets, two midterm exams and a final. Two meetings per week.

Requisite: MATH 111 or equivalent. Although the course will cover the necessary mathematics, some prior familiarity with vectors, matrices and basic linear algebra is useful. Fall semester. Professor Jagannathan.

The theories of relativity (special and general) and the quantum theory constituted the revolutionary transformation of physics in the early twentieth century. Certain crucial experiments precipitated crises in our classical understanding to which these theories offered responses; in other instances, the theories implied strange and/or counterintuitive phenomena that were then investigated by crucial experiments. After an examination of the basics of Special Relativity, the quantum theory, and the important early experiments, we will consider their implications for model systems such as a particle in a box, the harmonic oscillator, and a simple version of the hydrogen atom. We will also explore the properties of nuclei and elementary particles, study lasers and photonics, and discuss some very recent experiments of interest in contemporary physics. Three class hours per week.

Requisite: MATH 121 and PHYS 117 or 124. Fall semester. Professor Hall.

A variety of classic and topical experiments will be performed. In the area of fundamental constants, we will undertake a measurement of the speed of light, a determination of the ratio of Planck’s constant to the charge of the electron through the study of the photoelectric effect, and an experiment to obtain the charge-to-mass ratio of the electron. We will study the wave nature of the electron through a diffraction experiment. An experiment to measure optical spectra and another on gamma ray spectra will reveal the power of spectroscopy for exploring the structure of matter. Other experiments such as nuclear magnetic resonance, quantized conductance in nanocontacts, and properties of superconductors will give students an opportunity to experience laboratory practice in its contemporary form. Emphasis will be placed on careful experimental work and data-analysis techniques. One meeting a week of discussion plus additional, weekly self-scheduled laboratory work.

Requisite: PHYS 225 or consent of the instructor. Spring semester. Professor TBA.

The course will present the mathematical methods frequently used in theoretical physics. The physical context and interpretation will be emphasized. Topics covered will include vector calculus, complex numbers, ordinary differential equations (including series solutions), partial differential equations, functions of a complex variable, and linear algebra. Four class hours per week.

Requisite: MATH 121 and PHYS 117/124 or consent of the instructor. Fall semester. Professor Loinaz.

The basic laws of physics governing the behavior of microscopic particles are in certain respects simple. They give rise both to complex behavior of macroscopic aggregates of these particles, and more remarkably, to a new kind of simplicity. Thermodynamics focuses on the simplicity at the macroscopic level directly, and formulates its laws in terms of a few observable parameters like temperature and pressure. Statistical Mechanics, on the other hand, seeks to build a bridge between mechanics and thermodynamics, providing in the process, a basis for the latter, and pointing out the limits to its range of applicability. Statistical Mechanics also allows one to investigate, in principle, physical systems outside the range of validity of Thermodynamics. After an introduction to thermodynamic laws, we will consider a microscopic view of entropy, formulate the kinetic theory, and study several pertinent probability distributions including the classical Boltzmann distribution. Relying on a quantum picture of microscopic laws, we will study photon and phonon gases, chemical potential, classical and degenerate quantum ideal gases, and chemical and phase equilibria. Three class hours per week.

Requisite: PHYS 225 or consent of the instructor. Spring semester. Professor TBA.

This course begins with the foundation of classical mechanics as formulated in Newton’s Laws of Motion. We then use Hamilton’s Principle of Least Action to arrive at an alternative formulation of mechanics in which the equations of motion are derived from energies rather than forces. This Lagrangian formulation has many virtues, among them a deeper insight into the connection between symmetries and conservation laws. From the Lagrangian formulation we will move to the Hamiltonian formulation and the discussion of dynamics in phase space, exploring various avenues for the transition from the classical to the quantum theory. We will study motion in a central force field, the derivation of Kepler’s laws of planetary motion from Newton’s law of gravity, two-body collisions, and physics in non-inertial reference frames. Other topics may include the dynamics of driven, damped oscillators, and non-linear dynamics of chaotic systems. Three class hours per week.

Requisite: PHYS 227 or consent of the instructor. Fall semester. Professor Loinaz.

A development of Maxwell’s electromagnetic field equations and some of their consequences using vector calculus. Topics covered include: electrostatics, steady currents and static magnetic fields, time-dependent electric and magnetic fields, and the complete Maxwell theory, energy in the electromagnetic field, Poynting’s theorem, electromagnetic waves, and radiation from time-dependent charge and current distributions. Three class hours per week.

Requisite: PHYS 117 or 124 and PHYS 227 or consent of the instructor. Fall semester. Professor Hall.

Wave-particle duality and the Heisenberg uncertainty principle. Basic postulates of Quantum Mechanics, wave functions, solutions of the Schroedinger equation for one-dimensional systems and for the hydrogen atom. Three class hours per week.

Requisite: PHYS 225 and 343 or consent of the instructor. Spring semester. Professor TBA.

(Offered as PHYS 400, BIOL 400, BCBP 400, and CHEM 400.) How do the physical laws that dominate our lives change at the small length and energy scales of individual molecules? What design principles break down at the sub-cellular level and what new chemistry and physics becomes important? We will answer these questions by looking at bio-molecules, cellular substructures, and control mechanisms that work effectively in the microscopic world. How can we understand both the static and dynamic shape of proteins using the laws of thermodynamics and kinetics? How has the basic understanding of the smallest molecular motor in the world, ATP synthase, changed our understanding of friction and torque? We will explore new technologies, such as atomic force and single molecule microscopy that have allowed research into these areas. This course will address topics in each of the three major divisions of Biophysics: bio-molecular structure, biophysical techniques, and biological mechanisms.

Requisite: CHEM 161, PHYS 116/123, PHYS 117/124, BIOL 191 or evidence of equivalent coverage in pre-collegiate courses. Spring semester. Professor Carter.

Independent Reading Course. A full course.

Fall and spring semester.

Same description as PHYS 498. A single course.

Requisite: PHYS 498. Spring semester. The Department.

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