Bryn Mawr College Physics 302b-2010 -- Advanced Quantum Mechanics
Meets: TT 11:30-1:00, Park 337, recitation TBA

Lecturer: Walter F. Smith (610-896-1332, Park 344, KINSC L110)
Office hours at BMC: Mon 9:00-10:00, Tues 10:30-11:30, Wed 9:00-10:00,
Thurs 10:30-11:30 & 1:00-2:30, Fri 9:00-10:00
                        Office hours at HC:    Tues 2:00-3:00, Wed 10:30-11:30, Thurs 3:00-4:30          
           Fri 11:00-11:30, 1:30-3:00

Syllabus (choose a format) Web Page .. PDF .. Word Format

Assignments
Exams

# 1 (Due 1-28): Web page .. Word .. PDF
# 2 (Due 2-5): Web page .. Word .. PDF
# 3 (Due 2-12): Web page .. Word .. PDF
# 4 (Due 2-19): Web page .. Word ..
PDF
# 5 (due 3-5): 
Web Page .. PDF .. Word
#6 (due 3-19): 
Web Page .. PDF .. Word
#7 (due 3-26): Web Page .. PDF .. Word
#8 (due 4-9): Web Page .. PDF .. Word
#9 (due 4-16): Web Page .. PDF .. Word

#10 (due 4-23): Web Page .. PDF .. Word
#11 (due 4-30): 
Web Page .. PDF .. Word

Exam 1: coverage .. practice questions .. actual exam
Exam 2: coverage .. practice questions .. actual exam

 

Solutions for assignments and exams (password required)

Lecture summaries

Tuesday
Thursday

11-19-10 Web page .. Word .. PDF
electron spin and magnetic moment, Stern-Gerlach experiment

11-21-10 Web page .. Word .. PDF
What the Stern-Gerlach experiment tells us, analogy with polarized light, bras, inner products, probability amplitude and its connection to probability, review of complex numbers
11-26-10 Web page .. Word .. PDF
Complete basis, connection between expansion coefficients and measurement probabilities, ***analogy between quantum superpositions and ordinary vectors***, overall phase has no importance, expectation value, standard deviation
11-28-10 Web page .. Word .. PDF
General expansions in terms of basis states, Hilbert space, connection between wavefunctions and kets, column vector notation for kets, rotating kets, linear operators, adjoints of operators
2-2-10 Web page .. Word .. PDF
Eigenvalues & Eigenstates, Jz operator, eigenvalues of a Hermitian operator are real, identity operator, matrix representation of operators, multiplying operators, taking the adjoint in matrix notation
2-4-10 Web page .. Word .. PDF
Changing basis for operators in matrix notation, expectation values using matrix notation, commuting operators
2-9-10 Web page .. Word .. PDF
Diagonal operators; Commutators for Jx, Jy, and Jz; cyclic permutations; problems with our definitions of the spin kets; J2 operator; raising and lowering operators
2-11-10
Snow day
2-16-10 Web page .. Word .. PDF
Clarification about S-matrix, relation between magnitude and z-component of angular momentum, matrix elements for raising and lowering operators
2-18-10 Web page .. Word .. PDF
Generalized uncertainty relation, J vs. S, Pauli Spin Matrices, General procedure for soloving the eigenvalue problem
2-23-10 First half: exam review
Second half: Web page .. Word .. PDF
Time translation operator U, Hamiltonian operator H, time-dependent Schrodinger equation
2-25-10 Web page .. Word .. PDF
Energy eigenstates, time dependence of energy eigenstates, time dependence of expectation values for a generic state, precession of spin in a magnetic field, Berry phase, begin magnetic resonance
3-2-10 Web page .. Word .. PDF
Finish Magnetic resonance (ctd.), stimulated emission, absorption of photons, NMR and MRI, begin ammonia
3-4-10 Web page .. Word .. PDF
Finish ammonia (double-well potential), energy-time uncertainty, lack of time evolution of expectation values for energy eigenstates, connecting to the wavefunction, two spin-1/2 particles: basis, direct product
3-16-10 Web page .. Word .. PDF
Total Sz and S2 operators for two spin-1/2 particles
3-18-10 Web page .. Word .. PDF
Eigenstates of S2 operators for two spin-1/2 particles
(i.e. singlet and triplet states)
3-23-10 Web page .. Word .. PDF
Picturing the singlet and triplet states, general additional of angular momenta, the EPR paradox, quantum mechanics is non-local, hidden variable theory
3-25-10 Web page .. Word .. PDF
Bell's inequality, proof that hidden variable theories are wrong, position eigenstates, normalization and expectation values in the position basis, Dirac delta function, the translation operator, the momentum operator is the generator of translations
3-30-10
Exam review session
4-1-10 Web page .. Word .. PDF
The momentum operator in the x-basis, momentum eigenstates, De Broglie relations
4-6-10 Web page .. Word .. PDF
Blank Mathematica notebook for physics
Gaussian wavepackets, time-dependent and time-independent SEQin the x-basis, probability current, boundary conditions on y, begin scattering
4-8-10 Web page .. Word .. PDF
Mathematica notebook
Probability current for traveling waves, evanescent waves, tunneling through a square barrier, Scanning Tunneling Microscopy
4-13-10 Web page .. Word .. PDF
Tunneling through a non-square barrier, field emission, raising and lowering operators for the harmonic oscillator, energies for the harmonic oscillator
4-15-10 Web page .. Word .. PDF
Harmonic oscillator wavefunctions, torsional motion of ethylene
4-20-10 Web page .. Word .. PDF
Reduced mass, relative and total momentum, center of mass and relative motion, angular momentum in 3D

4-22-10 Web page .. Word .. PDF
Conservation of angular momentum, centrifugal barrier, Lz operator, eigenfunctions of Lz

handout: proof that rotation by 2p doesn't affect y
Web page .. Word .. PDF

4-27-10 Web page .. Word .. PDF
Spherical harmonics, non-degenerate perturbation theory

4-29-10 Web page .. Word .. PDF
Example of non-degenerate perturbation theory
, degenerate perturbation theory

handout: example of degenerate perturbation theory
Web page .. Word .. PDF


Handouts:
The S-matrix


Historical Notes, demonstrator applets, songs, etc.

Math Appendices -- Helpful mathematical material collected by Haverford and Bryn Mawr Physics majors some years ago, edited by Lyle Roelofs.

The Stern-Gerlach song: lyrics & chords .. mp3

Background image: The n = 4, l = 2, m = 1 state for hydrogen. The image shows an isosurface for the probability amplitude, with phase indicated by color. From the Visual Quantum Mechanics web page.