### Descriptions of courses required for the Physics major

Physics 17: Modern Physics

(4) Lecture, three hours; discussion, one hour. Requisites: Physics 1A, 1B, and 1C (or 1AH, 1BH, and 1CH). Corequisite: Physics 32. Photons, black-body radiation, photoelectric effect, uncertainty principle, Bohr atom, Schrödinger equation, hydrogen atom, and selected topics in atomic, solid-state, nuclear, and particle physics. P/NP or letter grading.

*Guidelines for topics to be covered in this class and suggested approximate schedules are listed below.*

**Textbook:**

“Modern Physics,” Serway, Moses, and Moyer (3rd ed., 2005)

Week | Topics | Chapters |
---|---|---|

1 | Black-body radiation, photoelectric effect, Compton scattering | 3 |

2 | Rutherford atom, Bohr’s model | 4 |

3 | De Broglie matter wave, uncertainty principle, wave-particle duality | 5 |

4 | Schrödinger equation, wave packets, particle in a box, finite quantum well | 6 |

5 | Harmonic oscillator, tunneling | 6,7 |

6 | SE in 3D, particle in a 3D box, hydrogen atom, Zeeman effect, electron spin | 8,9 |

7 | Atomic: L-S coupling, many-e atom, exclusion principle | 9 |

8 | Solids: structure and binding, free-electron model of metal, semiconductor | 12 |

9 | Nuclear binding and structure, radioactivity, fission, fusion | 13 |

10 | Particles and interactions, accelerators/detectors, quarks/gluons, standard model | 15 |

**Learning outcomes:** Advancing the knowledge of modern physics concepts and phenomena. The knowledge gained in a collection of modern physics topics will enable a better understanding of a range of applications in modern science and technology. The acquired analytical skills will also facilitate subsequent undergraduate research experience.

Physics 32: Mathematical Methods

(4) Lecture, three hours; discussion, one hour. Requisites: Physics 1A, 1B, and 1C (or 1AH, 1BH, and 1CH), Mathematics 32A/B and 33A. Corequisite: Mathematics 33B. Vectors and fields; operators and transformations; matrices, tensors, and differential forms; ordinary differential equations and integral theorems; Fourier transform. P/NP or letter grading.

This course is currently listed as Physics 131 (as of May 2021).

*Guidelines for topics to be covered in this class and suggested approximate schedules are listed below. *

**Textbook:**

“Mathematical Methods for Physicists,” Arfken, Weber, and Harris (7th ed., 2013)

Week | Topics | Chapters |
---|---|---|

1 | Linear algebra | 2 |

2 | Vector analysis | 3 |

3 | Differential operators and integral theorems | 3 |

4 | Tensors and differential forms (optional) | 4 |

5 | Vector spaces and linear operators | 5 |

6 | Matrix eigenvalues and diagonalization | 6 |

7 | Ordinary differential equations | 7 |

8 | Fourier series | 19 |

9 | Integral (Fourier/Laplace) transforms | 20 |

10 | (bonus) Transformations and symmetries in physics | 17 |

**Learning outcomes:** Developing proficiency in a broad range of mathematical methods that are applicable to a variety of physics problems in classical mechanics, electromagnetism, quantum mechanics, and thermal physics. The acquired mathematics skills will prepare students to succeed in the upper division physics core curriculum.

Physics 105A: Classical Mechanics

(4) Lecture, three hours; discussion, one hour. Requisite: Physics 32. Newtonian mechanics and conservation laws, gravitational potentials, calculus of variations, Lagrangian and Hamiltonian mechanics, central force motion, linear and nonlinear oscillations. Grading: P/NP or letter grading.

*Guidelines for topics to be covered in this class and suggested approximate schedules are listed below. *

**Textbook:**

“Classical Dynamics,” Thornton and Marion (5th ed., 2003)

Week | Topics | Chapters |
---|---|---|

1 | Newton laws, projectile | 1,2 |

2 | Conservation laws: Energy, momentum, angular momentum | 2 |

3 | Oscillations | 3 |

4 | Calculus of variation, Lagrangian | 6 |

5 | Lagrangian formalism, generalized coordinates | 7 |

6 | Conserved quantities, Hamiltonians | 7 |

7 | Phase space, Liouville theorem | 7 |

8 | Gravitation, central force | 5,8 |

9 | Two-body, celestial mechanics | 8 |

10 | (bonus) Nonlinear dynamical systems, chaos | 4 |

**Learning outcomes:** Ability to apply knowledge of classical mechanics to understand and analyze a broad variety of physical phenomena. Understanding and applying Lagrangian and Hamiltonian formalism to describe dynamical systems.

Physics 105B: Classical Mechanics

(4) Lecture, three hours; discussion, one hour. Requisite: Physics 105A. Conserved quantities, collisions and scattering, special relativity, non-inertial reference frames, rigid bodies, coupled oscillators and normal modes. Grading: P/NP or letter grading.

**Textbook:**

“Classical Dynamics,” Thornton and Marion (5th ed., 2003)

Week | Topics | Chapters |
---|---|---|

1 | Review of Hamiltonian/Lagrangian mechanics, conserved quantities | 7 |

2 | Collisions and scattering | 9 |

3 | Special theory of relativity: Lorentz transformations, 4-vectors | 14 |

4 | Relativistic momentum, relativistic collisions | 14 |

5 | Motion in noninertial reference frames | 10 |

6 | Rigid bodies (kinematics) | 11 |

7 | Rigid bodies (dynamics) | 11 |

8 | Coupled oscillators | 12 |

9 | Normal modes | 12 |

10 | (bonus) Continuous mechanics, waves | 13 |

**Learning outcomes:** Ability to apply knowledge of various aspects of classical mechanics to understand and analyze a broad variety of physical phenomena, including rigid bodies and coupled oscillators. Understanding of the rules to change reference frame to describe a dynamical system, including relativistic and noninertial cases.

Physics 110A: Electricity and Magnetism

(4) Lecture, three hours; discussion, one hour. Requisites: Physics 32. Electrostatics and magnetostatics. P/NP or letter grading.

**Textbook:**

"Introduction to Electrodynamics,” Griffiths (4th ed., 2017)

Week | Topics | Chapters |
---|---|---|

1 | Math refresh, electrostatics | 1,2 |

2 | Electrostatics | 2 |

3 | Electrostatics | 2 |

4 | Potentials | 3 |

5 | Potentials | 3 |

6 | Electrostatics in matter | 4 |

7 | Magnetostatics | 5 |

8 | Magnetostatics | 5 |

9 | Magnetic fields in matter | 6 |

10 | Magnetic fields in matter | 6 |

**Learning outcomes:** Ability to analyze physics problems involving static electric and magnetic fields, potentials and their sources.

Physics 110B: Electricity and Magnetism

(4) Lecture, three hours; discussion, one hour. Requisites: Physics 110A. Corequisite: Physics 105B. Maxwell’s equations, electromagnetic waves, potential and fields, radiation, Lorentz invariance. P/NP or letter grading.

**Textbook:**

“Introduction to Electrodynamics,” Griffiths (4th ed., 2017)

Week | Topics | Chapters |
---|---|---|

1 | Electrodynamics | 7 |

2 | Electrodynamics | 7 |

3 | Electrodynamics | 7 |

4 | Conservation laws | 8 |

5 | Electromagnetic waves | 9 |

6 | Electromagnetic waves | 9 |

7 | Potentials and fields | 10 |

8 | Potentials and fields | 10 |

9 | Radiation | 11 |

10 | Electrodynamics and relativity | 12 |

**Learning outcomes:** Mastering fundamental laws and concepts in electrodynamics encoded in Maxwell’s equations, as well as their implications such as electromagnetic waves and radiation.

Physics 112: Thermal Physics

(4) Lecture, three hours; discussion, one hour. Requisites: Physics 115A. Corequisite: Physics 115B. Fundamentals of thermodynamics and statistical mechanics. Classical and quantum ensembles. Simple applications including heat engines and pumps. Degenerate Fermi gases, Bose condensates, and blackbody radiation. P/NP or letter grading.

**Textbook:**

“An Introduction to Thermal Physics,” Schroeder (1st ed., 1999)

Week | Topics | Chapters |
---|---|---|

1 | First law, equipartition of energy, microcanonical ensemble | 1 |

2 | Entropy, temperature, and work; paramagnet and Einstein solid | 1,2 |

3 | Second law, generalized forces, pressure of ideal gas | 2,3 |

4 | Heat engines, pumps, and refrigerators; performance efficiencies | 4 |

5 | Thermodynamics with environment, thermodynamic potentials, Maxwell relations; phase transitions; van der Waals model | 5 |

6 | Canonical and grand canonical ensembles; Maxwell speed distribution | 6 |

7 | Partition function (ideal gas and paramagnet revisited) | 6 |

8 | Quantum statistics: Bosons vs fermions | 7 |

9 | Fermi gases and Bose-Einstein condensation | 7 |

10 | Blackbody radiation and Debye theory of solids | 7 |

**Learning outcomes:** Developing the foundational understanding of the principles of thermal and statistical physics and the ability to apply these principles to a set of representative physical examples. Be able to synergize the knowledge acquired from the entirety of the core physics education in the thermodynamic contexts.

Physics 115A: Quantum Mechanics

Units: 4.0 Lecture, three hours; discussion, one hour. Requisites: Physics 17, 105A. Classical background. Basic ideas of quantum nature of light, wave-particle duality, Heisenberg uncertainty principle, Schrödinger equation. One-dimensional square well and harmonic oscillator problems. One-dimensional scattering, Formal theory, Hilbert spaces and Dirac notation. P/NP or letter grading.

**Textbook:**

”Introduction to Quantum Mechanics,” Griffiths (3rd ed., 2017)

Week | Topics | Chapters |
---|---|---|

1 | Experimental motivation and phenomena leading to QM | |

2 | Schrödinger equation, probability interpretation | 1.1-1.3 |

3 | Normalization of wave function, momentum and uncertainty principle | 1.4-1.6 |

4 | Time-independent Schrödinger equation, infinite square well | 2.1-2.2 |

5 | Harmonic oscillator | 2.3 |

6 | Free particle and scattering | 2.4-2.5 |

7 | Finite square well, Hilbert space | 2.6-3.1 |

8 | Observables and spectra of operators | 3.2-3.3 |

9 | Generalized statistical interpretation and uncertainty principle | 3.4-3.5 |

10 | Dirac notation, extra time for a special topic | 3.6 |

**Learning outcomes:** Mastering the underlying mathematical structures and the physical principles of quantum mechanics, in particular the probabilistic nature of quantum mechanics, time evolution and measurements. Applying the principles of QM to simple one dimensional systems.

Physics 115B: Quantum Mechanics

Units: 4.0 Lecture, three hours; discussion, one hour. Requisite: Physics 115A. Corequisite: Physics 105B. Three-dimensional problems. Central potentials. Hydrogen atom. Angular momentum and spin, identical particles, and Pauli exclusion principle. Electrons in an electromagnetic field. Symmetries. P/NP or letter grading.

**Textbook:**

”Introduction to Quantum Mechanics,” Griffiths (3rd ed., 2017)

Week | Topics | Chapters |
---|---|---|

1 | 3-dim quantum mechanics, hydrogen atom | 4.1-4.2 |

2 | Hydrogen atom, cont. | 4.2 |

3 | Angular momentum | 4.3 |

4 | Spin | 4.4 |

5 | Addition of angular momentum, electromagnetic interactions | 4.5 |

6 | Identical particles, atoms, free electron gas | 5.1-5.3 |

7 | Symmetry, translation operators and conservations (quantum Noether theorem) | 6.1-6.3 |

8 | Parity and rotational symmetry | 6.4-6.5 |

9 | Degeneracy, selection rules, Heisenberg picture | 6.6-6.8 |

10 | EPR paradox and Bell’s theorem | 12.1-12.2 |

**Learning outcomes:** Application of the principles of quantum mechanics to three dimensional systems and multi-particle systems. Ability to calculate the energy levels of Hydrogen and related Atoms. Understanding the quantum mechanical realization of angular momentum and spin, including the addition of angular momentum. Understanding the importance and implementation of symmetries in quantum mechanics.

Physics 115C: Quantum Mechanics

Units: 4.0 Lecture, three hours; discussion, one hour. Requisite: Physics 115B. Time-independent perturbation theory, application to atomic spectra. Time-dependent perturbation theory. Fermi’s golden rule. Scattering. WKB approximation. P/NP or letter grading.

**Textbook:**

”Introduction to Quantum Mechanics,” Griffiths (3rd ed., 2017)

Week | Topics | Chapters |
---|---|---|

1 | Time-independent perturbation: Nondegenerate | 7.1 |

2 | Time-independent perturbation: Degenerate | 7.2 |

3 | Application to hydrogen spectrum | 7.3 - 7.4 |

4 | WKB approximation | 9 |

5 | Scattering | 10.1 - 10.2 |

6 | Scattering | 10.3 - 10.4 |

7 | Time-dependent Schrödinger equation for 2-level systems | 11.1 |

8 | Absorption and emission of radiation | 11.2 - 11.3 |

9 | Fermi’s golden rule, adiabatic approximation | 11.4 - 11.5 |

10 | Mixed states, no-cloning theorem, Schrödinger’s cat, or other special topics | 12.3 - 12.5 |

**Learning outcomes:** Ability to use approximation methods, such as time independent and time dependent perturbation theory, WKB approximation and Fermi’s Golden rule to calculate spectra, transition amplitudes and scattering cross sections for interacting systems. Application of quantum mechanical approximation methods in atomic, particle and condensed matter physics.