Bryn Mawr College Physics 302b2010
 Advanced Quantum Mechanics
Meets: TT 11:301:00, Park 337, recitation TBA
Lecturer: Walter
F. Smith (6108961332, Park 344, KINSC L110)
Office hours at BMC: Mon 9:0010:00, Tues 10:3011:30, Wed 9:0010:00,
Thurs 10:3011:30 & 1:002:30, Fri 9:0010:00
Office hours at HC: Tues 2:003:00, Wed 10:3011:30, Thurs 3:004:30
Fri 11:0011:30, 1:303:00
Syllabus (choose a format) Web
Page .. PDF ..
Word Format
Solutions
for assignments and exams (password required)
Lecture summaries
Tuesday

Thursday

111910 Web page .. Word .. PDF
electron spin and magnetic moment, SternGerlach experiment

112110 Web page .. Word .. PDF
What the SternGerlach experiment tells us, analogy with polarized light, bras, inner products, probability amplitude and its connection to probability, review of complex numbers 
112610 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 
112810 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 
2210 Web page .. Word .. PDF
Eigenvalues & Eigenstates, J_{z} operator, eigenvalues of a Hermitian operator are real, identity operator, matrix representation of operators, multiplying operators, taking the adjoint in matrix notation 
2410 Web page .. Word .. PDF
Changing basis for operators in matrix notation, expectation values using matrix notation, commuting operators 
2910 Web page .. Word .. PDF
Diagonal operators; Commutators for J_{x}, J_{y}, and J_{z}; cyclic permutations; problems with our definitions of the spin kets; J^{2} operator; raising and lowering operators 

21610 Web page .. Word .. PDF
Clarification about Smatrix, relation between magnitude and zcomponent of angular momentum, matrix elements for raising and lowering operators 
21810 Web page .. Word .. PDF
Generalized uncertainty relation, J vs. S, Pauli Spin Matrices, General procedure for soloving the eigenvalue problem 
22310 First half: exam review
Second half: Web page .. Word .. PDF
Time translation operator U, Hamiltonian operator H, timedependent Schrodinger equation 
22510 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 
3210 Web page .. Word .. PDF
Finish Magnetic resonance (ctd.), stimulated emission, absorption of photons, NMR and MRI, begin ammonia 
3410 Web page .. Word .. PDF
Finish ammonia (doublewell potential), energytime uncertainty, lack of time evolution of expectation values for energy eigenstates, connecting to the wavefunction, two spin1/2 particles: basis, direct product 
31610 Web page .. Word .. PDF
Total S_{z} and S^{2} operators for two spin1/2 particles 
31810 Web page .. Word .. PDF
Eigenstates of S^{2} operators for two spin1/2 particles (i.e. singlet and triplet states) 
32310 Web page .. Word .. PDF
Picturing the singlet and triplet states, general additional of angular momenta, the EPR paradox, quantum mechanics is nonlocal, hidden variable theory 
32510 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 
33010
Exam review session 
4110 Web page .. Word .. PDF
The momentum operator in the xbasis, momentum eigenstates, De Broglie relations 

4810 Web page .. Word .. PDF
Mathematica notebook
Probability current for traveling waves, evanescent waves, tunneling through a square barrier, Scanning Tunneling Microscopy 
41310 Web page .. Word .. PDF
Tunneling through a nonsquare barrier, field emission, raising and lowering operators for the harmonic oscillator, energies for the harmonic oscillator 
41510 Web page .. Word .. PDF
Harmonic oscillator wavefunctions, torsional motion of ethylene 
42010 Web page .. Word .. PDF
Reduced mass, relative and total momentum, center of mass and relative motion, angular momentum in 3D 
42210 Web page .. Word .. PDF
Conservation of angular momentum, centrifugal barrier, L_{z} operator, eigenfunctions of L_{z}
handout: proof that rotation by 2p doesn't affect y
Web page .. Word .. PDF

42710 Web page .. Word .. PDF
Spherical harmonics, nondegenerate perturbation theory 
42910 Web page .. Word .. PDF
Example of nondegenerate perturbation theory, degenerate perturbation theory
handout: example of degenerate perturbation theory
Web page .. Word .. PDF

Handouts:
The Smatrix
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 SternGerlach 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. 

