8.04 | Spring 2016 | Undergraduate

# Quantum Physics I

Video Lectures

## Part 2: Quantum Physics in One-dimensional Potentials

lec # topics
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)

Spring 2016
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