PH5100 Quantum Mechanics I

This is the course that I taught during Fall 2019. The class consisted of students from the first-year of the two-year M.Sc. program in Physics as well as the third-year of the five-year dual degree program in Physics at IIT Madras.

I followed a strict 3 lectures + 1 tutorial session. I ended up creating 14 problem sets in all.

Problem Sets

Problem Set 1 || Problem Set 2 || Problem Set 3 || Problem Set 4 || Problem Set 5 ||
Problem Set 6 || Problem Set 7 | Problem Set 8 || Problem Set 9 || Problem Set 10 ||
Problem Set 11 || Problem Set 12 || Problem Set 13 || Problem Set 14 ||

Some links

Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics History of the Stern-Gerlach experiment.

Wave function collapse vs the ensemble picture (Must see video) This video shows how these two views can co-exist!

Illustrating the variational method This is my class lecture typed up.

Official Course Syllabus

+ See course content

PH5100 Quantum Mechanics- I

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. Tunneling. 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. Non-degenerate and degenerate cases. Examples. Time-dependent perturbation theory. Transition probabilities. Sudden and adiabatic approximations. Fermi golden rule. The variational method: simple examples.

Course 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).