Quantum Mechanics

This course introduces the basic ideas of quantization in the physical world. Schrodinger wave equation: Born's interpretation of wave functions; expectation values; time-independent Schrodinger equation; required properties of eigenfunctions; energy quantization in Schrodinger theory; quantum superposition. Solutions of time-independent Schrodinger equation: Zero potential; step potential; barrier potential; quantum mechanical tunneling (radioactive ?-decay, ammonia molecule, tunnel diode, scanning tunneling microscope;); square well potential; simple harmonic oscillator potential. One-electron atoms: Central potential, development of the Schrodinger equation in 3-dimensions; separation of variables; eigenvalues, quantum numbers and degeneracy; eigenfunctions; probability densities; orbital angular momentum; eigenvalue equations. Magnetic dipole moments & spin: Orbital magnetic dipole moments; Stern-Gerlach experiment and electron spin; spin-orbit interaction; total angular momentum. Indistinguishable particles: Spin and Anti-symmetric wave functions; Bosons and Fermions. Formalism of Quantum Mechanics and Matrix Mechanics: Postulates of quantum mechanics; Dirac notation; Matrix representation of operators.