LEC # | TOPICS | KEY DATES |
---|---|---|
Part 1: Basic Concepts | ||
1 | Introduction: Basic features of quantum mechanics: Linearity, complex numbers, nondeterministic, superposition, entanglement. | |
2 | Two-slit experiments. Mach-Zehnder interferometer. Elitzur-Vaidman bombs. | |
3 | Photoelectric effect. Compton Scattering. de Broglie wavelength. | Problem Set 1 due |
4 | Galilean transformation of de Broglie wavelength. Wave-packets and group velocity. | |
5 | Matter wave for a particle. Momentum and position operators. Schrödinger equation. | Problem Set 2 due |
6 | Interpretation of the wavefunction. Probability density, probability current. Current conservation. Hermitian operators. | |
7 | Expectation values of ˆx. Wave-packets and uncertainty. Time evolution of wave-packets. Shape changes. Fourier transforms and Parseval Theorem. | Problem Set 3 due |
8 | Momentum expectation values. General definition of expectation values of Hermitian operators. Time derivative of expectation values (Ehrenfest theorem). Commutators. | |
9 | Hermitian operators as observables: Real eigenvalues orthogonal eigenfunctions. Measurement postulate. Uncertainty defined. Uncertainty relation stated. | Problem Set 4 due |
Part 2: Quantum Physics in One-dimensional Potentials | ||
10 | Stationary states. Boundary conditions for the wavefunction. Particle on a circle. | |
Exam 1 | ||
11 | Infinite square well. Basic properties of one-dimensional potentials. The finite square well. | |
12 | Turning points, semiclassical approximations, qualitative features of the wavefunction. | Problem Set 5 due |
13 | Numerical solution by the shooting method. | |
14 | Delta function potential. Discussion of the node theorem. Setup for the simple harmonic oscillator: Differential equation. | Problem Set 6 due |
15 | Analysis of the differential equation: Hermite polynomials. Algebraic solution of the harmonic oscillator with creation and destruction operators. | |
16 | Scattering states continued. Reflection and transmission coefficients. Constructing wave packets. Finding a particle in the forbidden region? | Problem Set 7 due |
17 | Ramsauer Townsend effect. Finite square well, resonant transmission. Scattering in 1D by finite range potentials. | |
Exam 2 | ||
18 | 1D Scattering and phase shifts. Example. Levinson’s theorem. | |
Part 3: One-dimensional Scattering, Angular Momentum, and Central Potentials | ||
19 | Resonances and Breit-Wigner distribution. The complex k-plane | Problem Set 8 due |
20 | Central Potentials and Angular momentum. Algebra of angular momentum. Simultaneous eigenstates of L_{z} and L^{2}. Legendre polynomials. | |
21 | QAssociated Legendre polynomials. Radial equation. Begin Hydrogen atom. 2-body problem and separation of variables. | Problem Set 9 due |
22 | Scales in the hydrogen atom. Differential equation: behaviors at infinity and at zero. Series solution. Energy quantization. | |
23 | Energy levels diagram for hydrogen. Virial theorem applied. Circular orbits and eccentricity. | Problem Set 10 due |
24 | More on orbits and turning points. The simplest quantum system and discovering spin | |
Final Exam |
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