8.04 | Spring 2016 | Undergraduate

Quantum Physics I

Video Lectures

Part 3: One-dimensional Scattering, Angular Momentum, and Central Potentials

lec # topics
Lecture 19: Resonances and Breit-Wigner distribution. The complex k-plane.
L19.1 Time delay and resonances (18:18)
L19.2 Effects of resonance on phase shifts, wave amplitude and time delay (14:53)
L19.3 Modelling a resonance (15:37)
L19.4 Half-width and time delay (08:17)
L19.5 Resonances in the complex k plane (15:14)
Lecture 20: Central potentials and angular momentum.
L20.1 Translation operator. Central potentials (19:13)
L20.2 Angular momentum operators and their algebra (14:28)
L20.3 Commuting observables for angular momentum (17:17)
L20.4 Simultaneous eigenstates and quantization of angular momentum (24:35)
Lecture 21: Legendre equation. Radial equation. Hydrogen atom 2-body problem.
L21.1 Associated Legendre functions and spherical harmonics (18:51)
L21.2 Orthonormality of spherical harmonics (17:57)
L21.3 Effective potential and boundary conditions at r=0 (14:28)
L21.4 Hydrogen atom two-body problem (25:04)
Lecture 22: Hydrogen atom (cont.). Differential equation, series solution and quantum numbers
L22.1 Center of mass and relative motion wavefunctions (14:22)
L22.2 Scales of the hydrogen atom (09:56)
L22.3 Schrödinger equation for hydrogen (20:59)
L22.4 Series solution and quantization of the energy (14:22)
L22.5 Energy eigenstates of hydrogen (12:24)
Lecture 23: Spectrum for hydrogen. Virial theorem, circular orbits and eccentricity.
L23.1 Energy levels and diagram for hydrogen (13:41)
L23.2 Degeneracy in the spectrum and features of the solution (14:20)
L23.3 Rydberg atoms (26:22)
L23.4 Orbits in the hydrogen atom (10:45)
Lecture 24: Hydrogen atom (conclusion). The simplest quantum system and emergent angular momentum.
L24.1 More on the hydrogen atom degeneracies and orbits (23:21)
L24.2 The simplest quantum system (13:55)
L24.3 Hamiltonian and emerging spin angular momentum (15:42)
L24.4 Eigenstates of the Hamiltonian (14:03)

Course Info

As Taught In
Spring 2016
Learning Resource Types
Lecture Videos
Problem Sets
Lecture Notes