Download 2012) all (F I

Day
Date
Topics
Mon 27 Aug Introduction; The Stern-Gerlach Experiment and its implications for the structure of nature
Wed 29 Aug Quiz 1;
Analysis of the Stern-Gerlach Experiment, and the analogy with polarized light
Thu 30 Aug The Formalism: Kets, bras, and operators
Mon
3 Sep No Classes: Labor Day
Wed
5 Sep Quiz 2;
Class cancelled: Instructor on travel
Thu
6 Sep Base kets and the matrix representation
Thu
6 Sep 6pm Makeup Class (JRSC 1C13): Measurements and observables
Mon 10 Sep Compatible and incompatible observables; the generalized uncertainty relation
Mon 10 Sep 6pm Makeup Class (JRSC 1C13): Change of basis; Unitary operators
Wed 12 Sep Quiz 3;
Class cancelled: Instructor on travel
Thu 13 Sep Class cancelled: Instructor on travel
Mon 17 Sep The position representation and the translation operator
Wed 19 Sep Quiz 4;
Momentum as generator of translations; Canonical commutation relations
Thu 20 Sep Wave functions of position and momentum, including three dimensions
Mon 24 Sep Motion of a wave packet
Wed 26 Sep Time evolution: The Hamiltonian as a generator of time translation;
time dependence of expectation values; the “Energy/Time” uncertainty relation
Thu 27 Sep Quiz 5; No lecture today: Instructor on travel
Mon
1 Oct The Schrödinger and Heisenberg pictures
Wed
3 Oct Quiz 6;
Formulating the simple harmonic oscillator
Thu
4 Oct Solving the simple harmonic oscillator with the operator formalism
Tue
9 Oct Schrödinger’s wave equation and interpreting the wave function
Wed 10 Oct Quiz 7;
Classical connections: Ehrenfest’s Theorem; the Hamilton-Jacobi Equation
Thu 11 Oct Solving the simple harmonic oscillator with Schrödinger’s Equation and generating functions
Modern Quantum Mechanics, Sakurai & Napolitano, Chapters 1,2,3
December 2, 2012
PHYS 6510/4510 Quantum Mechanics I (Fall 2012)
2.2; 2.4
2.5
2.2; 2.3
2.3
2.4
2.2
1.6
1.7
1.7
2.1
1.6
1.3
1.4
1.4
1.5
1.1
1.2
Textbook
1.1
18 Oct
22 Oct
24 Oct
25
29
29
31
1 Nov
5 Nov
7 Nov
8 Nov
12 Nov
14 Nov
15
19
21
22
26
28
29 Nov
3 Dec
5 Dec
6 Dec
Thu
Mon
Wed
Thu
Mon
Mon
Wed
Thu
Mon
Wed
Thu
Mon
Wed
Thu
Mon
Wed
Thu
Mon
Wed
Thu
Mon
Wed
Thu
Nov
Nov
Nov
Nov
Nov
Nov
Oct
Oct
Oct
Oct
Date
15 Oct
17 Oct
Day
Mon
Wed
Topics
More wave equation solutions: The free particle in Cartesian coordinate, and the linear potential
Quiz 8;
The WKB approximation for bound states in one dimension
Propagators, Green’s Functions, and the Schrödinger Wave Equation
Propagators and the connection to path integrals and classical physics
Quiz 9;
Class cancelled: Instructor on travel
Class cancelled: Instructor on travel
Potentials and gauge transformations in quantum mechanics
6pm Makeup Class (JRSC 1C13): The Aharonov-Bohm Effect and magnetic monopoles
Angular momentum as the generator of rotations in quantum mechanics
Finite rotations in spin-1/2; Rotations through 2π
Spin-1/2 using the Pauli two-component formalism
Class cancelled: Instructor on travel
Quiz 10;
The groups SO(3), SU (2), and Euler rotations
Density operators, ensembles, and quantum statistical mechanics
Eigenvalues and eigenstates of general angular momentum from the commutation relations
Quiz 11;
Orbital angular momentum and rotations in three spatial dimensions
Spherical harmonics
Schrödinger’s Equation solutions for spherically symmetric potentials
No Classes: Thanksgiving
No Classes: Thanksgiving
Examples: The free particle, the isotropic harmonic oscillator, and the Coulomb potential
Addition of angular momenta
Calculating Clebsch-Gordan coefficients
Deterministic alternatives to quantum mechanics, and Bell’s innequality
Vector operators
Vector, tensor, and spherical tensor operators
Matrix elements of tensor operators and the Wigner-Eckart Theorem
Applications of the Wigner-Eckart Theorem
3.7
3.8
3.8, 3.9
3.10
3.11
3.11
3.11
3.11
3.6
3.6
3.7
3.3
3.4
3.5
2.7
2.7
3.1
3.2
3.2
2.5
2.6
2.6
Textbook
2.5
Day Date
Topics
Wed 23 Jan Symmetries, conservation laws, and degeneracies; SO(4) and Pauli’s solution to the hydrogen atom
Continuous and discrete symmetries
Thu 24 Jan Space-inversion (parity) symmetry and applications in nature
Mon 28 Jan Lattice translation as a discrete symmetry and Bloch’s Theorem
Wed 30 Jan Quiz 1;
Time-reversal (“Reversal of motion”) symmetry: Formalism
Thu 31 Jan Phenomenology of time-reversal symmetry
Mon
4 Feb Time-independent, non-degenerate perturbation theory: Basic formalism
Wed
6 Feb Quiz 2;
Energies, states, and renormalization in time-independent perturbation theory; Basic examples
Thu
7 Feb First order degenerate time-independent perturbation theory; The linear Stark effect
Mon 11 Feb Second order degenerate time-independent perturbation theory
Wed 13 Feb Quiz 3;
Application to hydrogen-like atoms: The relativistic kinetic energy shift
Thu 14 Feb Application to hydrogen-like atoms: The spin-orbit interaction, Lande’s rule, and the sodium atom
Tue 19 Feb Application to hydrogen-like atoms: The Zeeman effect
Wed 20 Feb Quiz 4;
The variational method and its application to approximations
Thu 21 Feb Time-dependent potentials: The interaction picture
Mon 25 Feb Two-state problems with time-dependent potentials; Resonance phenomena
Wed 27 Feb Quiz 5;
The adiabatic approximation and Berry’s Phase
Thu 28 Feb Time dependent perturbation theory and Fermi’s Golden Rule
Mon 4 Mar Harmonic perturbations, and application to the classical radiation field
Wed 6 Mar Quiz 6;
Calculation of the photoelectric effect with the classical radiation field
Thu 7 Mar Energy shift and decay width
11-15 March: Spring Break
Modern Quantum Mechanics, Sakurai & Napolitano, Chapters 4 through 8
December 2, 2012
PHYS 6520/4520 Quantum Mechanics II (Spring 2013)
5.8
5.9
5.6
5.7
5.7, 5.8
5.4
5.5
5.5
5.3
5.3
5.3
5.1
5.2
Notes
4.4
4.4
5.1
Textbook
4.1
4.2
4.2
4.3
Day
Date
Topics
Mon 18 Mar Scattering as a time-dependent perturbation: Transition rate, cross section, and the T -matrix
Wed 20 Mar Quiz 7;
Solving for the T -matrix; Mathematical interlude on poles and residues in complex analysis
Thu 21 Mar Green’s Function for the Lippman-Schwinger Equation in coordinate space
Mon 25 Mar The scattering amplitude and the optical theorem
Wed 27 Mar Quiz 8;
The Born approximation
Thu 28 Mar Partial waves and the eikonal approximation
Mon
1 Apr Low-energy scattering and the connection to bound states
Wed
3 Apr Quiz 9;
Resonance scattering
Thu
4 Apr Identical particles and the symmetrization postulate
Mon
8 Apr Two-electron systems and the helium atom
Wed 10 Apr Quiz 10;
Multiparticle states in second quantization
Thu 11 Apr Example: The degenerate electron gas
Mon 15 Apr Quantization of the electromagnetic field
Wed 17 Apr Quiz 11;
The Casimir effect
Thu 18 Apr Fundamentals of quantum optics and “squeezed states”
Mon 22 Apr Relativistic quantum mechanics and the Klein-Gordon Equation
Wed 25 Apr Quiz 12;
Fixing the problem with negative energies: The Klein-Gordon Field
Thu 26 Apr The Dirac Equation and its elementary solutions
Mon 29 Apr Negative energies and the electromagnetic interactions of spin-1/2 particles
Wed 1 May Quiz 13;
Angular momentum and parity symmetry in the Dirac Equation
Thu
2 Apr Charge conjugation symmetry and time reversal symmetry in the Dirac Equation
Mon 6 May The Dirac Equation and the hydrogen atom
Wed 8 May Quiz 14;
The relativistic hydrogen atom spectrum and the evidence for quantum electrodynamics
8.4
8.3
8.3
8.4
Notes
8.2
8.2
7.6
7.5, Notes
8.1
7.5
7.5
7.6
6.7
7.1, 7.2
7.3, 7.4
6.3
6.4, 6.5
6.6
6.1; Notes
6.2
6.2
Textbook
6.1