This course treats those parts of quantum mechanics that lead to the description of a particle in a potential, of atoms, and of molecules. The concepts introduced and discussed will be the Schrödinger equation, wavefunctions, eigenvalues and eigenfunctions, spin, angular momentum, and Pauli's principle. The course is a basic introductory course that develops the formalism based on the Schrödinger equation and other Eigenvalue/Eigenfunction equations using the (differential) operators that represent physical observables, and then goes on to use it for a few physical systems, starting from one dimensional potential problems and then going on to the behavior of a particle in a central potential, atoms, and the simplest molecules.
After this course you should be able to understand and use the basic building blocks of quantum-mechanics, and to go on to discover more of the beauty of this amazing theory by following more advanced courses.
The course discusses the material presented in Chapters 5-10 and 12 of the textbook by Robert Eisberg and Robert Resnick: "Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles". Wiley 1985. ISBN: 978-0-471-87373-0.
The topics are the wavefunction and its meaning; Expectation values; The Schrödinger equation; the "time-independent" Schrödinger equation, which is an example of an eigenvalue/eigenfunction equation; The Hamilton operator and other operators for momentum and angular momentum; Other eigenvalue/eigenfunction equations using these operators; One-dimensional potential problems (quantum well, harmonic oscillator); The central potential. The hydrogen atom; Spherical harmonics; Spin; Exchange Symmetry; Fermions and Bosons; The addition of angular momenta; Triplet and Singlet states; Spin-Orbit coupling; Multi-electron atoms; Molecules; Vibrational and rotational states.