Quantum Mechanics Teaching Fall2014

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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)

Click here for the course outline.

Pre-mid term

1D quantum states.
1D quantum states.

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.

Reading suggestions:

Video recordings:

Creation, annihilation and number operators. [1]

Angular momentum in quantum mechanics, compatible observables. [2]

Time dependence of number states, time evolution. [3]

Coherent states. [4]

Hydrogenic wave functions.
Hydrogenic wave functions.

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

Recitation, reading suggestions and simulations:

Video recordings:

Angular part of Schrodinger equation for a central potential. [5]

Orbital angular momentum. [6]

Radial momentum operator, Rigid rotor[7]

DC Stark effect in Rydberg atoms.
DC Stark effect in Rydberg atoms.

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 [8]
Introducing the time-dependent perturbation theory [9]
DC Stark effect in hydrogen [10]
Ammonia molecule in an external electric field [11]
Expository session on time-dependent perturbation theory [12]

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

Reading suggestions

Please read in the same order,

Multi-particle states and operators [13]
Density operators and Bell states [14]
Applications of density operator concept [15]
Quantum mechanics: local or non local [16]
Applications of QM (Teleportation) [17]

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

Fine structure
Fine structure

Addition of Angular Momentums (2 lectures)

  • Two spin-1/2 systems
  • Hyperfine interactions
  • Coupled and uncoupled basis
  • Adding generalized angular momentums: good and bad quantum numbers
  • Clebsch-Gordan coefficients: Here is a chart showing Clebsch-Gordan coefficients.
  • Spin-orbit interaction

Addition of angular momentums [18]
Addition of generalized angular momentums [19]
Perturbations to the H-atom [20]
Zeeman effect [21]
Identical particles [22]

Final Exam

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