Quantum Mechanics for Materials Science

1. wave particle dualism particle character of light wave character of particles 2. wave mechanics Schrödinger equation wave functions 3. Mathemathical formalism of quantum mechanics Hilbert space observables statistical interpretation uncertainty principle Ehrenfest theorem uncertainty of energy and time Dirac notation 4. Example solutions General properties of the solutions, bound and scattering states infinite square well harmonic oscillator delta function potential well finite square well potential barrier and tunneling 5. Free electron description of solids Sommerfeld theory of the free electron gas free electrons in a periodic lattice the origin of energy gaps 6. Spherically symmetric potentials Schrödinger equation in spherical coordinates Analytical Solution of the angular equation the radial equation te angular momentum the spin addition of angular momenta mgnetic moments spin-orbit coupling 7. Many particle systems identical particles Pauli principle The Helium atom the periodic table and Hund's rules 8. Perturbation theory