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Prerequisites: Physics C and Physics B. Open to senior-level students only. Physics was formerly numbered Physics A. Recommended preparation: Physics A. Laboratory-lecture course covering practical techniques used in research laboratories. Physics was formerly numbered Physics Prerequisites: Physics A laboratory-lecture-project course featuring creation of an experimental apparatus in teams of about two.

The course will use a computer interface such as the Arduino. Physics was formerly numbered Physics B. Development of quantum mechanics. Wave mechanics; measurement postulate and measurement problem. Piece-wise constant potentials, simple harmonic oscillator, central field and the hydrogen atom. Three hours lecture, one-hour discussion session. Matrix mechanics, angular momentum, spin, and the two-state system. Approximation methods and the hydrogen spectrum. Identical particles, atomic and nuclear structures. Scattering theory. Prerequisites: Physics B and Physics A.

Quantized electromagnetic fields and introductory quantum optics. Symmetry and conservation laws. Introductory many-body physics. Density matrix, quantum coherence and dissipation. The relativistic electron. Three-hour lecture, one-hour discussion session. A project-oriented laboratory course utilizing state-of-the-art experimental techniques in materials science. The course prepares students for research in a modern condensed matter-materials science laboratory. Under supervision, the students develop their own experimental ideas after investigating current research literature.

With the use of sophisticated state-of-the-art instrumentation students conduct research, write a research paper, and make verbal presentations. Quantum mechanics and gravity. Electromagnetism from gravity and extra dimensions. Unification of forces. Quantum black holes. Properties of strings and branes. From time to time a member of the regular faculty or a resident visitor will give a self-contained short course on a topic in his or her special area of research. This course is not offered on a regular basis, but it is estimated that it will be given once each academic year.

Course may be taken for credit up to two times as topics vary the course subtitle will be different for each distinct topic. Students who repeat the same topic in Physics will have the duplicate credit removed from their academic record. Integrated treatment of thermodynamics and statistical mechanics; statistical treatment of entropy, review of elementary probability theory, canonical distribution, partition function, free energy, phase equilibrium, introduction to ideal quantum gases.

Prerequisites: Physics A. Applications of the theory of ideal quantum gases in condensed matter physics, nuclear physics and astrophysics; advanced thermodynamics, the third law, chemical equilibrium, low temperature physics; kinetic theory and transport in nonequilibrium systems; introduction to critical phenomena including mean field theory.

PHYS Prerequisites: upper-division standing. Applications of finite element PDE models are chosen from quantum mechanics and nanodevices, fluid dynamics, electromagnetism, materials physics, and other modern topics. Particle motions, plasmas as fluids, waves, diffusion, equilibrium and stability, nonlinear effects, controlled fusion.

Cross-listed with MAE A. Prerequisites: Math 20D. Physics of the solid-state. Binding mechanisms, crystal structures and symmetries, diffraction, reciprocal space, phonons, free and nearly free electron models, energy bands, solid-state thermodynamics, kinetic theory and transport, semiconductors. Prerequisites: Physics A or Chemistry Corequisites: Physics A. Physics of electronic materials. Semiconductors: bands, donors and acceptors, devices. Metals: Fermi surface, screening, optical properties. Superconductors: pairing, Meissner effect, flux quantization, BCS theory.

The constituents of matter quarks and leptons and their interactions strong, electromagnetic, and weak. Symmetries and conservation laws. Fundamental processes involving quarks and leptons. Unification of weak and electromagnetic interactions. Particle-astrophysics and the Big Bang.

Introduction to stellar astrophysics: observational properties of stars, solar physics, radiation and energy transport in stars, stellar spectroscopy, nuclear processes in stars, stellar structure and evolution, degenerate matter and compact stellar objects, supernovae and nucleosynthesis.

Physics , , , and may be taken as a four-quarter sequence for students interested in pursuing graduate study in astrophysics or individually as topics of interest. Topics will include metrics and curved space-time, the Schwarzchild metric, motion around and inside black holes, rotating black holes, gravitational lensing, gravity waves, Hawking radiation, and observations of black holes. The expanding Universe, the Friedman-Robertson-Walker equations, dark matter, dark energy, and the formation of galaxies and large scale structure.

Topics in observational cosmology, including how to measure distances and times, and the age, density, and size of the Universe. Topics in the early Universe, including the cosmic microwave background, creation of the elements, cosmic inflation, the big bang. An introduction to the structure and properties of galaxies in the universe. Topics covered include the Milky Way, the interstellar medium, properties of spiral and elliptical galaxies, rotation curves, starburst galaxies, galaxy formation and evolution, large-scale structure, and active galaxies and quasars.

Physics , , , and may be taken as a four-quarter sequence in any order for students interested in pursuing graduate study in astrophysics or individually as topics of interest. Project-based course developing tools and techniques of observational astrophysical research: photon counting, imaging, spectroscopy, astrometry; collecting data at the telescope; data reduction and analysis; probability functions; error analysis techniques; and scientific writing.

Recommended preparation: concurrent enrollment or completion of one course from Physics , , , or is recommended. The principles and clinical applications of medical diagnostic instruments, including electromagnetic measurements, spectroscopy, microscopy; ultrasounds, X-rays, MRI, tomography, lasers in surgery, fiber optics in diagnostics. A selection of experiments in contemporary physics and biophysics.

Students select among pulsed NMR, Mossbauer, Zeeman effect, light scattering, holography, optical trapping, voltage clamp and genetic transcription of ion channels in oocytes, fluorescent imaging, and flight control in flies. This course teaches how quantitative models derived from statistical physics can be used to build quantitative, intuitive understanding of biological phenomena. Case studies include ion channels, cooperative binding, gene regulation, protein folding, molecular motor dynamics, cytoskeletal assembly, and biological electricity.

A quantitative approach to gene regulation including transcriptional and posttranscriptional control of gene expression, as well as feedback and stochastic effects in genetic circuits. These topics will be integrated into the control of bacterial growth and metabolism. Recommended preparation: an introductory course in biology is helpful but not necessary. The use of dynamic systems and nonequilibrium statistical mechanics to understand the biological cell. Topics chosen from: chemotaxis as a model system; signal transduction networks and cellular information processing; mechanics of the membrane; cytoskeletal dynamics; nonlinear Calcium waves.

May be scheduled with Physics Information processing by nervous system through physical reasoning and mathematical analysis. A review of the biophysics of neurons and synapses and fundamental limits to signaling by nervous systems is followed by essential aspects of the dynamics of phase coupled neuronal oscillators, the dynamics and computational capabilities of recurrent neuronal networks, and the computational capability of layered networks.

Recommended preparation: a working knowledge of calculus and linear algebra. Undergraduate seminars organized around the research interests of various faculty members. Prerequisites: Physics 2A or Physics 4A. The Senior Seminar Program is designed to allow senior undergraduates to meet with faculty members in a small group setting to explore an intellectual topic in Physics at the upper-division level. Senior Seminars may be offered in all campus departments.

Topics will vary from quarter to quarter. Senior Seminars may be taken for credit up to four times, with a change in topic, and permission of the department. Enrollment is limited to twenty students, with preference given to seniors. Directed group study on a topic or in a field not included in the regular departmental curriculum. Prerequisites: consent of instructor and departmental chair. Independent reading or research on a problem by special arrangement with a faculty member.

Honors thesis research for seniors participating in the Honors Program. Research is conducted under the supervision of a physics faculty member. Prerequisites: admission to the Honors Program in Physics. Applications to: charged particle motion; central forces and scattering theory; small oscillations; anharmonic oscillations; rigid body motion; continuum mechanics. An introduction to mathematical methods used in theoretical physics. Special theory of relativity, covariant formulation of electrodynamics, radiation from current distributions and accelerated charges, multipole radiation fields, waveguides and resonant cavities.

Ensemble theory; thermodynamic potentials. Quantum statistics; Bose condensation. Interacting systems: Cluster expansion; phase transition via mean-field theory; the Ginzburg criterion. Prerequisites: Physics A-B. Corequisites: Physics C. Transport phenomena; kinetic theory and the Chapman-Enskog method; hydrodynamic theory; nonlinear effects and the mode coupling method.

Stochastic processes; Langevin and Fokker-Planck equation; fluctuation-dissipation relation; multiplicative processes; dynamic field theory; Martin-Siggia-Rose formalism; dynamical scaling theory. The first of a two-quarter course in solid-state physics.

Lower Division

Covers a range of solid-state phenomena that can be understood within an independent particle description. Topics include: chemical versus band-theoretical description of solids, electronic band structure calculation, lattice dynamics, transport phenomena and electrodynamics in metals, optical properties, semiconductor physics.

Deals with collective effects in solids arising from interactions between constituents. Topics include electron-electron and electron-phonon interactions, screening, band structure effects, Landau Fermi liquid theory. Magnetism in metals and insulators, superconductivity; occurrence, phenomenology, and microscopic theory.

Prerequisites: Physics A and Physics A.

Structure of Matter : A Survey of Modern Physics by Stephen Gasiorowicz (1979, Hardcover)

Quantum principles of state pure, composite, entangled, mixed , observables, time evolution, and measurement postulate. Simple soluble systems: two-state, harmonic oscillator, and spherical potentials. Angular momentum and spin. Time-independent approximations. Symmetry theory and conservation laws: time reversal, discrete, translation and rotational groups. In other words, modelling as a constructive teaching strategy seems absent. So, students think that neutrons must play a role here, which is true, but need to understand exactly how and why their hypotheses are wrong.

To cover these topics, the need of a strong force to solve question 2a must be discussed. Then, the spontaneous decay of nucleons and the interplay between the strong and weak interactions could be introduced to explain unstable nuclei and could be also used to introduce neutrinos. Block 3 is the block of questions with the worst results. But at the same time, this is showing how science concepts are not connected to the social context in science class, since these questions have had a significant diffusion on media over the last years.

Such considerations could be treated when introducing the interactions, in particular, when talking about gravity. These concerns should be clarified with easy models. Antimatter, danger, black holes and swallowing are concepts somehow related for students, probably due to the influence of science fiction films or books e. This combination of concepts, misconceptions, and arguments should be taken into consideration in order to create an effective communication with society. What are those particles?

How many of them can be observed? What for?

The structure of matter : a survey of modern physics

All these questions naturally appear. This points out that a teaching intervention strategy is needed. Finally, the level of knowledge of Block 4 is somehow high, showing that students understand some of the implications of particle physics and emphasize their interest in modern physics.

Finally, most of the students express their interest about including this kind of physics question 4d as part of the curriculum in different ways. Men scored better in this block. Interestingly, blocks of questions more directly related to academic contents Blocks 1 and 2 are the ones that show significant or marginally significant differences between high schools p-values 0. Contrary to what could be expected, students do have knowledge about particle physics despite not being covered by the traditional curricula.

However, this knowledge is partial, unstructured and there is a great variability among students and topics, which motivates the need of a teaching intervention strategy consistent with modelling techniques. The idea is not to add an extra item in the high school curriculum about Particle Physics, but to encourage teachers to lead the discussions about matter components and interactions beyond the 19th century until nowadays [ 25 ]. Most of these questions can easily fit into the current curricula.

For example, when studying atomic models, question 2b should trigger the discussion towards the need of the strong interaction and new particles quarks that can feel it and compose the protons. This also clarifies the role of the neutrons in the nucleus. Later in the course, when macroscopic forces like friction or the elastic force appear, it is important to recall that all these forces can be understood in terms of the fundamental ones; and that almost all macroscopic forces have an electric origin. Further investigation is needed to provide effective teaching interventions that could help to bridge the gap from the 19th century physics taught in High Schools to modern and up-to-date ideas of Nature.

In this paper, the level of knowledge about the structure and interactions of matter has been evaluated, according to whether or not this knowledge shows an updated view of the topic. The knowledge of students adjusts globally to a mid-low level, i. However, the variability of answers is high. Ideas from new models appear, meaning that students somehow know updated concepts. Nonetheless, these ideas are very tentative and show confusions with both new and classical models.

Our results show that students are highly interested towards particle physics and they are curious about the social implications of the topic. The whole picture justifies the need of a teaching intervention strategy to integrate the new concepts in the learning process; so that the classical models can be correctly understood and the topic about matter turns out to be unbiased and completed. Given the social impact of modern physics, this necessity is reinforced.

However, how this can be done in an effective manner has been barely investigated see [ 9 ] and references therein. Our goal for a further study is to present a teaching intervention strategy. It is based on interactive engagement [ 26 ] and modelling techniques with embodiment [ 27 ].

Using embodiment , students perform as the active agents of the model, which greatly facilitates the understanding and learning process. Tables 1, 2, 3 and 4 describe the answers categories for Block 1 , 2 , 3 and 4 of questions from the pretest. The tables show, for each question referenced on the first column, the different types of answers considered as categories second column , their corresponding score third column and the percentage of students answers that fit into that category fourth column. We wish to acknowledge the students, teachers and high schools involved in this study for their kind participation.

We also want to thank Javier Montero-Pau for constructive feedback. National Center for Biotechnology Information , U. PLoS One. Published online Jun 2. Alejandro Raul Hernandez Montoya, Editor. Author information Article notes Copyright and License information Disclaimer. Competing Interests: The authors have declared that no competing interests exist.

Received Nov 11; Accepted May This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. S2 File: Questionnaire. Blank copy of the questionnaire given to students. The test was composed by 17 questions divided into four main blocks: Block 1 about atomic structure and interactions: a What is matter made of? Results and Discussion The description of the sample according to gender and elective for the six groups of students is found in Table 1.

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Table 1 Summary of the sample size N and sample distribution according to group, high school, gender and elective, where Bio means Biology and Tech means Technical Drawing, for each group of students. Open in a separate window. Fig 1. Global results for each of the 17 questions. Conclusions In this paper, the level of knowledge about the structure and interactions of matter has been evaluated, according to whether or not this knowledge shows an updated view of the topic.

PDF Click here for additional data file. S2 File Questionnaire. Acknowledgments We wish to acknowledge the students, teachers and high schools involved in this study for their kind participation. Funding Statement The authors have no support or funding to report. Data Availability All relevant data are within the paper and its Supporting Information files. References 1. Solbes J, Traver M. Introduction to nonrelativistic quantum mechanics: perturbation theory, the variational principle, radiation; application of quantum mechanics to atomic physics, magnetic resonance, scattering, and various special topics.

PHYS Optics Laboratory 3 NW Measurements of interference and diffraction, optical properties of matter, image processing, interferometry, holography. Building a microprocessor application. Provides background for teaching physical science as a process of inquiry and develops scientific literacy. Background for teaching physics at secondary school and introductory college levels. Some mathematical proficiency required.

Prerequisite: a minimum 2. Numerical exercises to illustrate phenomena. Prerequisite: MATH PHYS Quantum Physics 4 NW Introduction to concepts and methods of quantum physics: wave mechanics de Broglie wavelength, uncertainty principle, Schrodinger equation , one-dimensional examples tunneling, harmonic oscillator , formalism of quantum physics, angular momentum and the hydrogen atom.

Focuses on participation, barriers to participation, and solutions to those issues for women and ethnic minorities in physical sciences and engineering. Offered: jointly with GWSS Written and oral presentations summarizing work accomplished are required.

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PHYS Mechanics 3 Lagrangian and Hamiltonian dynamics, with applications to various topics such as coupled oscillators, parametric resonance, anharmonic oscillations, chaos. PHYS Numerical Methods 3 Integration, solution of differential equations, Monte Carlo methods, function minimization, data analysis, modern computing techniques, computation in experimental physics.

PHYS Physical Applications of Group Theory 3 Applications of finite and continuous groups, representation theory, symmetry, and conservation laws to physical systems. Principles of electrostatics, complex variable techniques, boundary value problems and their associated mathematical techniques, Green's functions. Electric and magnetic fields in free space and material media, wave guides and cavity resonators. Special relativity, electromagnetic radiation from accelerated charges, synchrotron radiation, Cerenkov radiation, radiation reaction.

Modern non-relativistic quantum mechanics developed, beginning with its basic principles. Dirac and abstract operator notation introduced, starting with simple examples. Modern non-relativistic quantum mechanics. The character of the theory illustrated both with physical examples and with conceptual problems. Topics include: atomic structure, scattering processes, density operator description of mixed states, and measurement theory. Abstract operator methods emphasized in the exposition of angular momentum, scattering, and perturbation theory. Physical examples and conceptual problems.

PHYS Advanced Quantum Mechanics - Introduction to Quantum Field Theory 4 Multi-particle systems, second quantization, diagrammatic perturbation theory, radiation, correlation functions and multi-particle scattering, relativistic theories, renormalizability, basic quantum electrodynamics, and other applications. PHYS Advanced Quantum Mechanics - Introduction to Quantum Field Theory 3 Multi-particle systems, second quantization, diagrammatic perturbation theory, radiation, correlation functions and multi-particle scattering, relativistic theories, renormalizability, basic quantum electrodynamics, and other applications.

PHYS Thermodynamics and Statistical Mechanics 4 Statistical mechanical basis of the fundamental thermodynamical laws and concepts; classical and quantum statistical distribution functions; applications to selected thermodynamic processes and examples of Bose and Fermi statistics. PHYS Statistical Mechanics 3 Introduction to equilibrium and non-equilibrium aspects of many-body systems; scale invariance and universality at phase transitions and critical phenomena; exactly soluble models; Markov processes, master equations and Langevin equation in non-equilibrium stochastic processes.

Topics may include continuous and pulsed lasers; solid, liquid, and gas gain media; Q-switching, mode-locking, resonator theory, nonlinear optics, and others. Prerequisite: basic quantum mechanics, electromagnetism, and optics. Phases, phase transitions, optical and dielectric properties, molecular and device "engineering," future prospects.

PHYS Introduction to Acoustics and Digital Signal Processing 4 Introduces mathematical and physics principles of acoustics in digital signal processing applications. Complex analysis and Fourier methods, physics of vibrations and waves, solutions of the wave equation, digital convolution and correlation methods, and Maximum Length Sequence method in signal analysis and spread-spectrum applications.

PHYS Applications of Quantum Physics 4 Techniques of quantum mechanics applied to lasers, quantum electronics, solids, and surfaces. Emphasis on approximation methods and interaction of electromagnetic radiation with matter. Topics may include integration, differential equations, partial differential equations, optimization, data handling, and Monte Carlo techniques.

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Emphasis is applications in physics. Prerequisite: 30 credits in physical sciences, computer science, or engineering.