Quantum Mechanics Teaching Spring2014

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Contents


Quantum Mechanics I


Instructor: Dr. [Sabieh Anwar] Office hours: are Monday and Wednesday, 4 to 5 pm.

Teaching Fellows: [Aroosa Ijaz] Office hours: Monday (10:00 am to 12:00 noon), [Mustafa Afzal Saeed] Office hours: Thursday (10:00 am to 12:00 noon) and [Kaneez Amna]. Aroosa and Mustafa will be available in the Physics Department's lounge at the available times.

Textbooks: "Quantum Mechanics: Theory and Experiment" by Mark Beck. (Primary textbook). Three copies are available in the Course Reserve section in the LUMS Library. Copies of the supplementary textbook "Quantum Mechanics: Concepts and Applications" are also available in the Coourse Reserve Section.


Click here for the course outline. Homeworks, quizes and exams have been temporarily suppressed from the website.


Pre-mid term

Classical Description of Polarization (3 lectures)

A set of cascaded polarizers, whose transmission axis successively differs by ϕ/M.
A set of cascaded polarizers, whose transmission axis successively differs by ϕ/M.
  • The Polarization Vector
  • Linear, Circular, Elliptical Polarization
  • Birefringent Materials
  • Manipulating polarization through optical elements

Here is an interesting list of animations showing the polarization states of light.

Quantum States (2 lectures)

  • Quantum Interference
  • Inner product
  • Basis states
  • Experiments with beam splitters

Quantum Operators (3 lectures)

Performing a polarization measurement using nondestructive photon detectors.
Performing a polarization measurement using nondestructive photon detectors.
  • Unit, Unitary, Hermitian operators
  • Projection, Rotation operators
  • Basis transformation
  • Representation of states and operators

Measurement (2 lectures combined as one)

  • Postulates of quantum mechanics
  • Von Neumann measurements
  • State preparation, measurement outcomes and their probabilities
  • Indeterminacy relations between non-commuting observables
  • Special Drill: (date=25 February 2014; 7:00 pm - 8:45 pm) Drill Session on quantum operators


Video recordings:

Unit, adjoint, rotation, projection operators. [1]

Representing states and operators, Similarity transformation.[2]

Change of Bases, Hermitian operators, real eigenvalues.[3]

Spectral decomposition of Hermitian operators, Measurement outcomes, Indeterminacy principle.[4]


Spin-1/2 (3 lectures)

Rotation on Bloch sphere
Rotation on Bloch sphere
  • The Stern-Gerlach experiment
  • Spin states
  • Interference of spin states
  • Commutation relations for spin angular momentum operators
  • Bloch sphere, rotations on the Bloch sphere
  • Single qubit logic gates (NOT and Hadamard gates)

Video recordings:

Force on a Magnetic Dipole, Interference of spin states. [5]

Commutation relations, Bloch sphere.[6]

Single spin-1/2 quantum gates. [7]




Post-mid term

Angular Momentum in Quantum Mechanics (3 lectures)

  • Compatible observables
  • Simultaneous eigenbasis
  • Generalized angular momentum
  • Eigenvalues and eigenstates of angular momentum


Video recordings:

Compatible observables, Simultaneous eigenbasis, Spin-1/2 angular momentum. [8]

Generalized angular momentum. [9]

Exemplifying the angular momentum. [10]



The Schrödinger Equation (4 lectures)

Muon spin rotation.
Muon spin rotation.
  • Temporal evolution of quantum states
  • Solutions to Schrödinger Equation
  • Temporal evolution of expectation values
  • Magnetic Resonance
  • Muon spin rotation
  • NMR Experiment
  • Rabi Oscillations


Tutorial and reading suggestions:



Video recordings:

Solution to time dependent Schrödinger Equation , temporal evolution of expectation values.[11]

Magnetic Resonance. [12]

NMR experiment, Rabi flipping. [13]

Muon spin rotation. [14]


The Wavefunction (3 lectures)

  • Wavefunction
  • Dirac delta function
  • Wavefunction of a position eigenstate
  • Position and momentum states
  • Translation operator
  • Position-momentum uncertainty
  • Fourier transforms



Meaning of the wavefunction, wavefunction of a position eigenstate. [15]

Measuring momentum, position-momentum commutator. [16]

Momentum basis, momentum eigenstate in position basis, Fourier transforms. [17]


Wave Mechanical Formulation of Schrödinger Equation (3 lectures)

  • The Schrödinger equation in the position basis
  • The time-independent Schrödinger equation
  • Potential step and barriers
  • Infinite square well
  • Tunneling and its applications

Supplementary material and simulations:



The Schrödinger equation in position basis, Potential step. [18]

Scattering and tunneling. [19]

Radioactivity, Wavepackets. [20]



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