Detailed Schedule for PHYSI-125, Fall 2019
Unit Schedule (reproduced from Syllabus)
- Unit 1: Townsend Appendix A, and Chapters 1, 2, and 3 (Stern-Gerlach experiment, basis states, rotation operators, angular momentum)
- Unit 2: Townsend Chapters 4, 6, and 7 (time evolution, nuclear magnetic resonance, position space wave function, harmonic oscillator)
- Unit 3: Townsend Chapters 5 and 9 (two-particle states, hyperfine splitting of positronium, two-body orbit problem, spherical harmonics)
- Unit 4: Townsend Chapters 10 and 12 (Coulomb potential, hydrogen atom spectrum, identical particles, multi-electron atoms)
Unit 1 Detailed Schedule
Unit 1 Class Topics
- 2019-09-04: Review of electromagnetism following Appendix A of Townsend (culminating in the statement of Maxwell's laws in differential and integral form in the exceedingly elegant Heaviside-Lorentz units), torque on a current loop
- 2019-09-06: Potential for a current loop in a magnetic field, g-factor (relating magnetic moment and spin angular momentum), deflection of a current loop in a magnetic field gradient, the result of the Stern-Gerlach experiment, introduction of the kets for spin (and magnetic moment) along +z and -z
- 2019-09-09: Review Stern-Gerlach, review states, (Townsend Eqns. 1.29, 1.xx, 1.30 and 1.31), Example (Problem 1.3b), theory of uncertainty (defined mean and variance), uncertainty example (Example 1.2), review formalism (Townsend eqns. 1.33-1.47).
- 2019-09-11: Complete proof Townsend eqn. 1.41), *overall* phases don't matter for experimental results, active rotations vs. passive rotations, rotation operators as exponentials of spin operators, representation of kets as column vectors, bras as row vectors, and operators as matrices
- 2019-09-13: A day of examples (drawn from homework due 09-13)
- 2019-09-16: Hermitian conjugation, Hermitian operators (example, the Pauli matrices), unitary operators
- 2019-09-18: Non-commutativity of rotations (at 2nd order), commutator, anti-commutator.
- 2019-09-20: Commutation relations relations for the spin operators, eigenvalues and eigenstates of commuting operators.
- 2019-09-23: Raising and lowering operators (J+ and J-), simultaneous eigenvalues of J^2 and Jz characterized by j and m, introduced a set of three 3x3 matrices that implements j=1, m=+1, 0, and -1.
- 2019-09-25: A day of examples (mostly drawn from homeworks due 9-20 and 9-25).
- 2019-09-27: Unit 1 Midterm.
Unit 1 Homework Assignments
- HW01 (due 09-06): An elaborate — 9-part — breakdown of Townsend Problem 1.2.
- HW02 (due 09-09): Townsend Problems 1.3, 1.4.
- HW03 (due 09-13): 4 problems on properties of Jx, Jy, and Jz followed by Townsend Problems 2.5 and 2.6.
- HW04 (due 09-16): Townsend Problems 2.7, 2.8, 2.10, 2.11.
- HW05 (due 09-20): Townsend Problems 3.3, 3.4, 3.8, 3.10.
- HW06 (due 09-23): Townsend Problems 3.1 and also show Jx and Jy commute with Jx^2 + Jy^2 + Jz^2.
- HW07 (due 09-25): Townsend Problems 3.13, 3.15, and 3.17. (To do 3.15, first study 3.104 to 3.115.)
Unit 2 Detailed Schedule
Unit 2 Class Topics
- 2019-09-30: Begin Townsend sections 4.1 and 4.2.
- 2019-10-02 Finish 4.2, including examples 4.1 and 4.2 as group board work.
- 2019-10-04: Watch MRI video, review results from Townsend Sections 4.2 and 4.3, begin Townsend Section 4.4 (got to Eqn. 4.39).
- 2019-10-07: Finish Townsend Section 4.4. Begin Appendix C (the Dirac delta function)
- 2019-10-09: Finish Appendix C, and cover Townsend Section 6.1 (position-space wave functions).
- 2019-10-11: Appendix D (Gaussian integrals), go over essentials of Rabi's formula solution, begin Townsend sections 6.2, 6.3, and 6.4 (translation operator and momentum operator in the position basis, Hamiltonian for a particle in a potential)
- 2019-10-14: Finish Townsend sections 6.2, 6.3, and 6.4, and cover Townsend section 6.5 (momentum operator in the momentum basis, Fourier transforms, time evolution of Gaussian wave packets)
- 2019-10-16: Cover Townsend sections 6.6, 6.8, and 6.9 (Townsend section 6.7 was covered in modern)
- 2019-10-18: Raising and lowering operator method for solving the harmonic oscillator (Townsend 7.1, 7.2, and 7.3)
- 2019-10-21: Properties of position-space harmonic oscillator wave functions (Townsend 7.4, 7.5 and 7.7)
- 2019-10-23: Unit 2 midterm.
Unit 2 Homework Assignments
- HW08 (due 10-02): Problems 1 and 2 are Townsend 4.2 and 4.3. Problem 3: put H from Townsend Eqn. 4.17 into exp(-iHt/hbar), then put the Pauli matrix expression for S_z in, and simplify (like you did in the second exam problem)
- HW09 (due 10-07): Townsend 4.6, Townsend 3.2, Townsend 4.8, Symon #50
- HW10 (due 10-09): 1. Prove Rabi's formula (Townsend Problem 4.9), 2. Normalize two fairly common wave functions: (a) a cosine and (b) a gaussian).
- HW11 (due 10-14): A problem where you compute the average position x for some Gaussians using equation 6.14 (see handout)
- HW12 (due 10-16): Townsend 6.4, 6.5, and 6.6.
- HW13 (due 10-18): Townsend 6.9, 6.13, and 6.15.
- HW14 (due 10-21): Townsend 7.1, 7.2, 7.3, and 7.4.
Unit 3 Detailed Schedule
Unit 3 Class Topics
- 2019-10-28: Go over 2nd midterm in detail.
- 2019-10-30: Townsend Section 5.1 (two-particle systems, direct product).
- 2019-11-01: Townsend Section 5.2 (hyperfine splitting of positronium).
- 2019-11-04: Townsend Section 5.3 (systems with two spin states), classical two-body system, started Townsend 9.1 (quantum mechanics in 3-d, momentum in 3-d)
- 2019-11-06: Finish Townsend 9.1 and cover 9.2 (systems with two particles in 3-d, total momentum in 3-d)
- 2019-11-08: Townsend Section 9.3 (relative and center of mass coordinates)
- 2019-11-11: Townsend Section 9.5 (orbital angular momentum operators and angular momentum conservation), and 9.6 (eigenstates of L^2 and Lz, rewriting p^2 in terms of L^2 and p_radial)
- 2019-11-13: Townsend 9.8, L^2 in spherical coordinates.
- 2019-11-15: Townsend 9.9, Ylm(theta, phi) (spherical harmonics), Townsend example 9.3 (precession of px orbital around z-axis).
- 2019-11-18: Unit 3 midterm.
Unit 3 Homework Assignments
Unit 3 Midterm
Unit 4 Detailed Schedule
Unit 4 Class Topics
- 2019-11-20: Townsend Sections 10.1 and 10.2 (general properties of radial wave functions at small r, properties of Coulomb potential wave functions at large r)
Unit 4 Homework Assignments
- HW21 (due 11-22): Townsend Problems 10.1 and 10.2
Final (Unit 4 material and cumulative)