Introductory Quantum Mechanics

Part 1: the need for the quantum mechanics; quantization of radiation; the special theory of relativity; wave-particle duality; the nature of matter waves; the uncertainty principle; the Bohr atom. Part 2 Schrodinger's equation: the postulates of quantum mechanics; the wave equation; the wave equation in three dimensions; the time-independent Schrodinger equation; stationary states; normalisation; probability flux; physical constraints on the wave-function; wave packets; Gaussian wave-packets and the uncertainty principle. Part 3 One-dimensional potential wells: potential wells; the one-dimensional infinite square well; discussion of infinite square-well results; eigenvalue equations; the finite square well; finite square well eigenfunctions; the control of the wave-function by the wave equation; numerical integration of Schrodinger's equation; continuum solutions of the square-well potential; interpretation of unbound-particle wave functions; the double potential well; the quantum bouncer; electric fields and the tilted well; the harmonic oscillator - introduction; the quantum oscillator; discussion of harmonic oscillator eigenvalues and eigenfunctions; the classical probability density; more potential wells. Part 4 Schrodinger's equation in three dimensions: particle in a three dimensional box; degeneracy; Schrodingers equation in spherical polar coordinates - the hydrogen atom; normalisation. Part 5 Formal development of quantum mechanics: eigenvalues equations, operators and measurements; the momentum operator, eigenvalues and eigenfunctions; the position operator and its eigenfunctions; Hermitian operators; orthogonality of eigenfunctions; the expansion postulate; example - the b-decay of tritium; expectation values; compatibility of observables - commutators; non-commuting operators; time-dependence of expectation values - Ehrenfest's theorem; abstract operators - the parity operator, matrix mechanics. Part 6 Angular momentum: angular momentum operators; angular momentum commutators; angular momentum eigenvalues and eigenfunctions; interpretation of angular momentum eigenvalues; interpretation of angular momentum eigenfunctions; the Stern-Gerlach apparatus and electron spin; spin operators - the Pauli Spin matrices; the Zeeman effect; measurements in quantum mechanics. Part 7 Spherically symmetric potential wells: the rigid rotator; the radial equation; the hydrogen atom and hydrogen like ions; the isotropic harmonic oscillator; molecular vibrations - the Morse potential; the spherical square well; general properties of spherically symmetric potential wells. (Part contents)