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: RamsauerTownsend effect. Scattering in 1D.

L17.1

Waves on the finite square well (15:44)

L17.2

Resonant transmission (17:49)

L17.3

RamsauerTownsend 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)
