Fundamentals of Physics, II - Audio Ramamurti Shankar

The various postulates of quantum mechanics treated in previous lectures are reviewed and summarized. The uncertainty principle is again discussed and a new one between energy and time is introduced. The quantum mechanical behavior of an electron in a hydrogen atom is described. The principles of quantum mechanics are then generalized to describe two or more quantum particles. It is shown that identical particles have to be bosons or fermions, the latter obeying the Pauli exclusion principle, which in turn is key to explaining the periodic table.

The time-dependent Schrödinger Equation is introduced as a powerful analog of Newton's second law of motion that describes quantum dynamics. It is shown how given an initial wave function, one can predict the future behavior using Schrödinger's Equation. The special role of stationary states (states of definite energy) is discussed.

The allowed energy states of a free particle on a ring and a particle in a box are revisited. A scattering problem is studied to expose more quantum wonders: a particle can tunnel into the classically forbidden regions where kinetic energy is negative and a particle incident on a barrier with enough kinetic energy to go over it has a nonzero probability to bounce back.

It is shown how to extract the odds for getting different values of momentum from a generic wave function by writing it as a sum over functions of definite momentum. A recipe is given for finding states of definite energy, which requires solving a differential equation that depends on what potential the particle is experiencing. The particle in a box is considered and the allowed energies derived.

The fact that the wave function provides the complete description of a particle's location and momentum is emphasized. Measurement collapses the wave function into a spike located at the measured value. The quantization of momentum for a particle on a ring is deduced.

Lecture begins with a detailed review of the double slit experiment with electrons. The fate of an electron traversing the double slit is determined by a wave putting an end to Newtonian mechanics. The momentum and position of an electron cannot both be totally known simultaneously. The wave function is used to describe a probability density function for an electron. Heuristic arguments are given for the wave function describing a particle of definite momentum.