8.04 | Spring 2016 | Undergraduate
Quantum Physics I

## Calendar

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 Lz and L2. 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