Quantum Mechanics I

This is the homepage for the course PH5100 which I am teaching during Fall 2011 to first-year M.Sc. as well as third-year dual degree M.S. students at IIT Madras.

Objectives: This is the first course of two courses in quantum mechanics. It introduces the students to basic aspects of quantum mechanics.

Assessment

Two scheduled quizzes	20x2	40%
Final	60x1	60%
Total		100%

Assignments

There will be several ungraded assignments that will be handed out to the student.

Notes and Handouts

Online Resources

Read chapters 2 and 3 of Jim Hefferon's free book on Linear Algebra
Prof. Balakrishnan's Resonance Article on the Dirac Delta Function;
Prof. Tan's notes on Fourier Series and Transforms;
Prof. Tan's notes on Hilbert Spaces;
Observe the Gibbs phenomenon in the Fourier Series for the square wave;

Official syllabus

+ See course content

Basic principles of quantum mechanics. Probabilities and probability amplitudes. Linear vector spaces. Bra and ket vectors. Completeness, orthonormality, basis sets. Change of basis. Eigenstates and eigenvalues. Position and momentum representations. Wavefunctions, probability densities, probability current. Schrodinger equation. Expectation values. Generalized uncertainty relation.

One dimensional potential problems Particle in a box. Potential barriers. Tunnelling.

Linear harmonic oscillator: wavefunction approach and operator approach.

Motion in three dimensions. Central potential problem. Orbital angular momentum operators. Spherical harmonics. Eigenvalues of orbital angular momentum operators.

The hydrogen atom and its energy eigenvalues.

Charged particle in a uniform constant magnetic field, energy eigenvalues and eigenfunctions. Schrodinger and Heisenberg pictures Heisenberg equation of motion. Interaction picture.

Semiclassical approximation: the WKB method

Time-independent perturbation theory. Nondegenerate and degenerate cases. Examples.

Time-dependent perturbation theory. Transition probabilities. Sudden and adiabatic approximations. Fermi golden rule.

The variational method: simple examples.

References:

1. E. Merzbacher, Quantum Mechanics, 2nd Edition, Wiley International Edition (1970).
2. V.K. Thankappan, Quantum Mechanics. Wiley Eastern (1985)
3. J.J. Sakurai, Modern Quantum Mechanics, Benjamin Cummings (1985).
4. R.P. Feynman, R.B. Leighton and M.Sands, The Feynman Lectures on Physics, Vol.3, Narosa Pub. House (1992).
5. P.M. Mathews and K. Venkatesan, A Textbook of Quantum Mechanics, Tata McGraw-Hill (1977).