Views
Click here to go back to Teaching page
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)
Click here for the course outline.
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.
Reading suggestions:
- Slides on nanoresonator.
- Lecture notes on symmetries.
- Introduction to symmetry.
- Transformations and symmetries in quantum mechanics.
- Discrete symmetries, parity or space inversion.
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]
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:
- Solving the Angular part of the Schrodinger Equation.
- Solving the radial Schrodinger equation under central potential
- List of some low order spherical harmonics, radial wavefunctions and their plots
- Recitation: (date=15 September 2014; 3:30 pm - 4:45 pm) deals with radial wave function.
- Recitation: (date=22 September 2014; 3:30 pm - 4:45 pm) deals with wavefunctions of the hydrogen atom. Solution
- Now here is a link to a nice java applet that let's you visualize the wavefunctions of the hydrogen atom.
Video recordings:
Angular part of Schrodinger equation for a central potential. [5]
Orbital angular momentum. [6]
Radial momentum operator, Rigid rotor[7]
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:
- Recitation: (date=29 September 2014; 3:30 pm - 4:45 pm) deals with nondegenerate theory .
- Recitation: (date=13 October 2014; 3:30 pm - 4:45 pm) deals with degenerate theory .Solution
- Quiz: (date=15 October 2014; 8:00 am) Quiz 2 and its solution
- Recitation: (date=20 October 2014; 3:30 pm - 4:45 pm) deals with an alternative view of time-dependent perturbation theory.
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,
- Quantum mysteries for anybody. [N. D. Mermin, American Journal of Physics, 49, 940 (1981)]
- Chapter 1 A Brutal Fact of Life Lectures on Quantum Mechanics - Basic Matters by Berthold-Georg Englert. This is a great read.
- Spooky action at a distance in quantum mechanics. [L. Hardy, Contemporary Physics 39(6), 419-429 (1998)]
- Quantum mysteries refined. [N. David Mermin, American Journal of Physics 62, 880 (1994)]
- Quantum information and computation. [Charles H. Bennett & David P. DiVincenzo, Nature, Vol. 404 (2000)]
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
- Quiz: (date=12 November 2014; 8:00 am) Quiz 3 and its solution
- Homework: (date=5 December 2014; 5 pm) HW-4 and it solution
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]
- Recitation (date=1 December 2014; 3:30 pm - 4:45 pm) deals with Addition of generalized angular momentums Solution
- Quiz: (date=8 December 2014; 3:30 pm) Quiz-4