| Lecture 10: Uncertainty (cont.). Stationary states. Particle on a circle. |
| L10.1 |
Uncertainty and eigenstates (15:53) |
| L10.2 |
Stationary states: key equations (18:43) |
| L10.3 |
Expectation values on stationary states (09:00) |
| L10.4 |
Comments on the spectrum and continuity conditions (13:09) |
| L10.5 |
Solving particle on a circle (11:05) |
| Lecture 11: Uncertainty (cont.). Stationary states. Particle on a circle. |
| L11.1 |
Energy eigenstates for particle on a circle (16:12) |
| L11.2 |
Infinite square well energy eigenstates (13:15) |
| L11.3 |
Nodes and symmetries of the infinite square well eigenstates. (09:43) |
| L11.4 |
Finite square well. Setting up the problem. (22:30) |
| L11.5 |
Finite square well energy eigenstates (10:39) |
| Lecture 12: Properties of 1D energy eigenstates. Qualitative properties of wavefunctions. Shooting method. |
| L12.1 |
Nondegeneracy of bound states in 1D. Real solutions (12:36) |
| L12.2 |
Potentials that satisfy V(-x) = V(x) (14:18) |
| L12.3 |
Qualitative insights: Local de Broglie wavelength (15:52) |
| L12.4 |
Correspondence principle: amplitude as a function of position (05:53) |
| L12.5 |
Local picture of the wavefunction (12:52) |
| L12.6 |
Energy eigenstates on a generic symmetric potential. Shooting method (15:26) |
| Lecture 13: Delta function potential. Justifying the node theorem. Simple harmonic oscillator. |
| L13.1 |
Delta function potential I: Preliminaries (16:14) |
| L13.2 |
Delta function potential I: Solving for the bound state (15:21) |
| L13.3 |
Node Theorem (13:01) |
| L13.4 |
Harmonic oscillator: Differential equation (16:45) |
| L13.5 |
Behavior of the differential equation (10:31) |
| Lecture 14: Simple harmonic oscillator II. Creation and annihilation operators. |
| L14.1 |
Recursion relation for the solution (12:25) |
| L14.2 |
Quantization of the energy (23:23) |
| L14.3 |
Algebraic solution of the harmonic oscillator (16:50) |
| L14.4 |
Ground state wavefunction (15:58) |
| Lecture 15: Simple harmonic oscillator III. Scattering states and step potential. |
| L15.1 |
Number operator and commutators (15:49) |
| L15.2 |
Excited states of the harmonic oscillator (18:19) |
| L15.3 |
Creation and annihilation operators acting on energy eigenstates (21:03) |
| L15.4 |
Scattering states and the step potential (10:34) |
| Lecture 16: Step potential reflection and transmission coefficients. Phase shift, wavepackets and time delay. |
| L16.1 |
Step potential probability current (14:59) |
| L16.2 |
Reflection and transmission coefficients (08:12) |
| L16.3 |
Energy below the barrier and phase shift (18:40) |
| L16.4 |
Wavepackets (20:51) |
| L16.5 |
Wavepackets with energy below the barrier (05:54) |
| L16.6 |
Particle on the forbidden region (06:48) |
| Lecture 17: Ramsauer-Townsend effect. Scattering in 1D. |
| L17.1 |
Waves on the finite square well (15:44) |
| L17.2 |
Resonant transmission (17:49) |
| L17.3 |
Ramsauer-Townsend phenomenology (10:16) |
| L17.4 |
Scattering in 1D. Incoming and outgoing waves (18:05) |
| L17.5 |
Scattered wave and phase shift (08:40) |
| Lecture 18: Scattering in 1D (cont.). Example. Levinson’s theorem. |
| L18.1 |
Incident packet and delay for reflection (18:52) |
| L18.2 |
Phase shift for a potential well (09:13) |
| L18.3 |
Excursion of the phase shift (15:16) |
| L18.4 |
Levinson's theorem, part 1 (14:46) |
| L18.5 |
Levinson's theorem, part 2 (09:30) |
