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Physics 105 Analytic Mechanics (Zi Qiu):

Jerry B. Marion & Stephen T. Thorton, Classical Dynamics of Particles and Systems

Other Book:

L. D. Landau & E. M. Lifshitz, Mechanics

Alexei Deriglazov, Classical Mechanics: Hamiltonian and Lagrangian Formalism

Physics 110A Electromagneticism and Optics (Liang Dai):

John David Jackson, Classical Electrodynamics

Other Book:

Andrew Zangwill, Modern Electrodynamics

Physics 112 Introduction to Statistical and Thermal Physics (Austin Hedeman):

Daniel V. Schroeder, An Introduction to Thermal Physics

Charles Kittel & Herbert Kroemer, Thermal Physics

Frederick Reif, Fundamentals of Statistical and Thermal Physics

Physics 137A Quantum Mechanics (Irfan Siddiqi):

David J. Griffiths, Introduction to Quantum Mechanics

B.H. Bransden & C.J. Joachain, Quantum Mechanics

Other Book:

L. D. Landau & E. M. Lifshitz, Quantum Mechanics

Physics 139 Special Relativity and General Relativity (Lawrence Hall):

James B. Hartle, Gravity: An Introduction to Einstein's General Relativity

Bernard Schutz, A First Course in General Relativity

Sean M. Carroll, Spacetime and Geometry: An Introduction to General Relativity

Physics 151 Special Topic: Quantum Field Theory (Hitoshi Murayama):

Physics 205A Advanced Dynamics (Edgar Knobloch):

J.V. José & E.J. Saletan, Classical Dynamics, A Contemporary Approach

Physics 231 General Relativity (Yasunori Nomura):

Robert M. Wald, General Relativity

Physics 233A Standard Model and Beyond I (Ben Safdi):

Michael E. Peskin & Daniel V. Schroeder, An Introduction to Quantum Field Theory

Matthew D. Schwartz, Quantum Field Theory and the Standard Model

Stuart Raby, Introduction to the Standard Model and Beyond: Quantum Field Theory, Symmetries and Phenomenology

Several Courses:

Moataz H. Eman, Covariant Physics: From Classical Mechanics to General Relativity and Beyond

Physics 105 Analytic Mechanics:

David Morin The Lagrangian Method

S. Widnall & J. Peraire MIT 16.07 Dynamics Fall 2008 Lecture L5 - Other Coordinate System

David Kunbiznˇák, PSI Study Text: Theoretical Mechanics

Physics 110A Electromagneticism and Optics:

David Tong Electromagneticism

The Spherical Harmonics

Physics 112 Introduction to Statistical and Thermal Physics:

David Tong Statistical Physics

David Tong Statistical Field Theory

Mehran Kardar, MIT 8.333 Statistical Mechanics I: Statistical Mechanics of Particles, Fall 2013

Laws of Thermaldynamics, Wikipedia

Physics 137A Quantum Mechanics:

Robert Littlejohn's Physics 221AB Quantum Mechanics Lecture Recordings and Notes

Physics 139 Special Relativity and General Relativity:

Frederick Schuller's Lecture on General Relativity

Frederick Schuller's Lecture on General Relativity Notes

David Tong General Relativity

Physics 151 Special Topic: Quantum Field Theory:

Physics 231 General Relativity:

Physics 233A Standard Model and Beyond I:

Differential Geometry and Lie Groups for Physicists, Marián Fecko

David Tong Statistical Mechanics Note Ch. 1 - Ch. 3, https://www.damtp.cam.ac.uk/user/tong/statphys.html

Field Theory: Path Integral Approach, Ashok Das,  Ch. 1 - Ch2

PHYSICS 221AB Quantum Mechanics: http://bohr.physics.berkeley.edu/classes/221/2021/221.html Notes 1-11

Griffiths QM 7.1 and Section 7.3.0-7.3.1 (problem 7.17)

https://www.theoretical-physics.net/dev/index.html

Spring 2022 Physics Notes (Google Drive)

Physics 105 Analytic Mechanics:

105 Notes

Lecture 4 Newtonian Mechanics

Lecture 6 Damped Oscillator & Forced Oscillator

Lecture 7 Gravitation

Lecture 8 Gravitational Field, Force, & Potential

Lecture 9 Gravitational Potential & Energy

Lecture 9 Variations

Lecture 11 Variations

Lecture 11 Construction of Lagrangian

Lecture 12 Lagrangian and Three Examples

Lecture 13 Derivation of Hamiltonian, Equation of Moti0n, & Poisson Bracket

Lecture 14 Hamiltonian, Equations of Motion, Conservation of Momentum

Physics 110A Electromagneticism and Optics:

Instructor Liang Dai's Lecture Notes 1 Mathematics

Instructor Liang Dai's Lecture Notes 2 Electrostatics

110A March 8 Multipole Expansion

110A March 10 Polarization, Bound Charge

110A March 15 Polarization, Electric Displacement Vector

110A March 29 Electric Displacement, Linear Dielectric

Physics 112 Introduction to Statistical and Thermal Physics:

112 Lec 1

Physics 137A Quantum Mechanics:

Griffiths QM 3 Formalism

137A Lec 1

137A Lec 2

137A Feb 28

137A Mar 2

137A Mar 7

137A Mar 9

137A Mar 11-18 Third

Physics 139 Special Relativity and General Relativity:

205 Lec2

205 Lec3

205 Lec6

205 Lec8

205 Lec9

205 Lec10

205 Dis Jan 25

205 Dis Feb 1

205 Dis Feb 15

Physics 231 General Relativity:

Physics 233A Standard Model and Beyond I (Audit):

233A Lec 1

233A Lec 2

233A Lec 3

233A Lec 4

233A Lec 5

233A Lec 6

233A Feb 14

233A Feb 16

233A Feb 25

233A Feb 28

233A Mar 4

233A Mar 7

233A Mar 28

233A Apr 4

Lec 1 Thermodynamics

First Law: If A & C systems, B & C systems have the same temperature. A & B systems have the same temperature.

Second Law: In an adiabatic process (there is no heat transfer), the work chance is equal to the (final E - initial E). If there is heat transfer, ∆Q = (Final E - Initial E) - ∆W

In differential form

dE(\vec(x))          =        \bar(d) W + \bar(d) Q

Depends on state         Depend on path

Quasistatic: Slow (slow enough to maintain equilibrium)

Pull a string sufficient slowly that the string does not start to vibrate (Too rapidly -> oscillating)

Calculate the amount of work

\bar(W) = \Sigma_i J_i dx_i

\Sigma_i Generalized Force

\dx_i Generalized Path

x.       J

wire(1d)        L.      F

film(2d)        A.      \sigma (surface tension)

gas(3d).        V.      -P

Magnet.       M.      B.

x - extensive

J - intensive

\bar(d)W = \Sigma J_i dx_i

\bar(d)Q = ?

--

dE = \Sigma_i J_i dx_i + ?

Ideal gas scale:

Heat capacity C_{path}= \bar(d)Q_{path}/dT  \bar -> dependent on path

C_v C_p

C_v = \bar(d)Q_v/dT = (dE + PdV_v)/dT = ∂E/∂T|_v No mechanic work is done

C_p = \bar(d)Q_p/dT = (dE + PdV_p)/dT = ∂E/∂T|_p + P(∂V/∂T)|_p

Expansion ideal gas

A gas that is adiabatically isolated.

From a chamber to both chambers.

T_f = T_i = T

∆Q = 0 = ∆W -> ∆E

Pressure and volume certainly changed when it goes from one chamber to both chambers.

Ideal gas

E(P, V) = E(T, V)

C_p - C_v = PV/T = N k_b

k_B = 1.4 * 10^{-23}

Lec2 Thermodynamics

RECAP

A. Equilibrium (x_i, J_i)

x_i generalized displacement

J_i generalized force

Ideal Gas

(V, -P)

Where does it lie in the PV-Plane

B. 0th Laws (Transitive of Equilibrium) If two objects are in equilibrium with the third object they are also in equilibrium with each other

\Theta(x_i, J_i) = \Theta'(x_i', J_i')

The equilibrium has to be the same

Like a balance

(V, -P)

PV = \Theta (constant)

C. 1st laws

The amount of the work is only dependent on the initial and final state.

Conversation of Energy

\exist E(x_i, J_i)

dE = \bar(d)W+ \bar(d)Q

dE only depends on the state

\bar(d) blah depends on the path

Doole's free expansion

Isolate two gases into two chambers

Initial the gas is completely isolated on one side

Final the gas is on both sides

T_f = T_i

E must only be a product of PV

P changes V changes

But PV is constant

NEW

Quasistatic: slow enough:

\bar(d) W = \Sigma_i J_i dx_i (when the spring is pulled slowly aka. without vibrations)

mechanical equilibrium J is the same

\bar(d) Q =

temperature for measuring thermal equilibrium

the conjugate? Entropy

Student Qs:

[The equilibrium is ideal

D. 2nd law

Heat <- -> Work

Engine

Hot

| Q_H

V

Engine -> W

| Q_C

V

Cold

Efficiency

\ita = W/Q_H = (Q_H - Q_C)/Q_H < 1

Reverse Refrigerator

Performance

\omega = Q_c / W = Q_c / (Q_H - Q_c)

Kelvin: No process is possible whose sole result is complete conversion of heat to work.

(No idea engine, \ita < 1)

Clausius: No process is possible whose sole result is transfer of heat from colder to  hotter body. (No ideal refrigerator)

E. Carnot Engine is any engine that is

(1) Reversible: Can go forward/backward by reversing input/output (frictionless)

(2) Operates in cycle (start and endpoints are the same)

(3) All heat input and output at 2 temperature

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