# Quantum Mechanics Teaching Fall2014

## Contents

Quantum Mechanics II

Instructor: Dr. [Sabieh Anwar] Office hours: TBA.

Textbooks: "Quantum Mechanics: Theory and Experiment" by Mark Beck. (Primary textbook). "A Modern Approach to Quantum Mechanics" by John S. Townsend. (Useful complementary book)

## Pre-mid term

Harmonic Oscillator (4 lectures)

• Creation and annihilation operators
• Number states and number space
• Wavefunction in position space of | n ⟩
• Time dependence of number states
• Coherent states
• Time evolution of coherent states.

Recitations and Simulations:

• Recitation: (date=1 September 2014; 3:30 pm - 4:45 pm) deals with the harmonic oscillator in position space.
• A nice java applet that that shows the behavior of a single particle in bound states in one dimension. It solves the Schrödinger equation and allows you to visualize the solutions can be downloaded from here.
• Recitation: (date=8 September 2014; 3:30 pm - 4:45 pm) Parity, space-inversion, symmetry and degeneracy.

Video recordings: Creation, annihilation and number operators. 

Angular momentum in quantum mechanics, compatible observables. 

Time dependence of number states, time evolution. 

Coherent states. 

Wave Mechanics in Three Dimensions (4 lectures)

• Central potential
• Solving the radial, polar and azimuthal wave functions under central potential
• Orbital angular momentum
• Rotational symmetry and conservation of angular momentum

Video recordings: Angular part of Schrodinger equation for a central potential. 

Orbital angular momentum. 

Perturbation Theory (5 lectures)

• Time-independent perturbation for degenerate and non-degenerate states
• First-Order Corrections, second-Order Corrections
• Examples; Sloping infinite well, harmonic oscillator inside an electric field, DC Stark effect, ammonia molecule in an external electric field
• Time-dependent perturbation theory, transition probabilities
• Examples: sinusoidal perturbation, photoelectric effect, Einstein coeffcients

Recitations and quiz: Nondegenerate time-independent perturbation theory 
Introducing the time-dependent perturbation theory 
DC Stark effect in hydrogen 
Ammonia molecule in an external electric field 
Expository session on time-dependent perturbation theory 

## Post-mid term

Multi-Particle Systems, Entanglement, Nonlocality (5 lectures)

• Entanglement, Bell states
• Density matrices, traces, reduced density operators
• States of two-particle systems
• Application of density operators: Liouville von Neumann equation, thermal states, magnetization of a paramagnetic ensemble of spins
• Teleportation, no-cloning theorem Multi-particle states and operators 
Density operators and Bell states 
Applications of density operator concept 
Quantum mechanics: local or non local 
Applications of QM (Teleportation) 

Homework: (due date=10 November 2014; 5:00 pm) Homework on Density Operators and its Solution.
Recitation: (date=10 November 2014; 3:30 pm - 4:45 pm) deals with density operators Solution
Recitation: ( date=17 November 2014; 3:30 pm - 4:45 pm) deals with Quantum correlations and Bell's inequalities Solution

Addition of Angular Momentums (2 lectures)

• Two spin-1/2 systems
• Hyperfine interactions
• Coupled and uncoupled basis
• Clebsch-Gordan coefficients: Here is a chart showing Clebsch-Gordan coefficients.
• Spin-orbit interaction 