Frequently Asked Questions
I will try to answer here your main questions from lecture (not just
"frequently asked" ones, but any well-posed questions). Please ask
again if anything is still not clear!
Note I will occasionally go back later and add to or amend an answer.
- August 25 FAQ 1 Particles and waves: pdf html
- August 27 FAQ 2 Vector spaces, linear independence, inner products, bras and kets, adjoint operations: pdf html
- September 1 FAQ 3 Linear operators, matrix representations, projection operators: pdf html
- September 3 FAQ 4 Unitary and Hermitian matrices, active and passive transformations, eigenvectors and eigenvalues, diagonalization: pdf html
- September 8 FAQ 5 Coupled classical oscillator example, infinite dimensional vector spaces: pdf html
- September 10 FAQ 6 Dirac delta functions, Hilbert space, operators in Hilbert space, eigenfunctions of the K operator: pdf html
- September 15 FAQ 7 More on K and X operators, classical mechanics review, Poisson brackets: pdf html
- September 17 FAQ 8 Postulates of quantum mechanics: pdf html
- September 22 FAQ 9 Expectation value, uncertainty, compatible and incompatible operators, momentum space wavefunctions: pdf html
- September 24 FAQ 10 Momentum eigenfunctions, Schrödinger equation, propagators, stationary states: pdf html
- September 29 FAQ 11 Free Hamiltonian solutions, Gaussian wavepacket propagation pdf html
- October 8 FAQ 12 Continuity conditions, particle-in-a-box, energy quantization, continuity equation pdf html
- October 13 FAQ 13 Equation of continuity, probability current, potential step example: pdf html
- October 15 FAQ 14 Classical limits: pdf html
- November 3 FAQ 19 Direct product, identical particles, symmetrization and antisymmetrization: pdf html
- November 5 FAQ 20 Canonical transformations, consequences of symmetries in CM and QM, translation invariance: pdf html
- November 10 FAQ 21 Time translation, parity, parity invariance: pdf html
- November 17 FAQ 22 Angular momentum, rotational invariance in 2D and 3D, spherical harmonics, radial equation: pdf html
- November 19 FAQ 23 Hydrogen atom wavefunction solutions pdf html
- November 24 FAQ 24 Angular momentum ladder operators, angular momentum eigenvalues, orbital, spin and total angular momentum pdf html
- December 1 FAQ 25 Spin pdf html