The exhaustive list of topics in Quantum Mechanics in which we provide Help with Homework Assignment and Help with Project is as follows:

- Motivations for studying quantum mechanics.
- Simple harmonic oscillator; raising and lowering operators.
- Coherent states.
- Scattering theory in one dimension; reflection and transmission.
- Formation of bands in a periodic potential.
- Rotation group in three dimensions.
- Orbital angular momentum; algebra of generators of rotation.
- Spherical harmonics.
- Spin angular momentum; spin-1/2 and Pauli matrices.
- Hydrogen atom and its spectrum.
- Three-dimensional simple harmonic oscillator.
- Additional symmetries of hydrogen atom and simple harmonic oscillator.
- Spin-orbit and hyperfine interactions in hydrogen atom.
- Electron in an electromagnetic field; Aharonov-Bohm effect.
- Electron on a ring; persistent current.
- Electron in a magnetic field; Landau levels.
- Time-independent perturbation theory.
- Stark effect.
- Zeeman effect.
- Wigner-Eckart theorem.
- Effect of spin-orbit and hyperfine interactions.
- Identical particles: bosons and fermions.
- Multi-electron atoms.
- Molecules: rotations and vibrations.
- Scattering theory in three dimensions.
- Scattering from a hard sphere.
- Time dependent problems; sudden and adiabatic; Landau-Zener transition.
- Geometric phase.
- Fermi golden rule.
- Maxwell's equations and second quantisation.
- Spin angular momentum of photons.
- Coupling of electrons to an electromagnetic field.
- Density matrices.
- Kernel in quantum mechanics.
- Path integral formulation of quantum mechanics.