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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.