Principles of Quantum Mechanics

On successful completion of this module students should be able to:

1. Present and classify the basic principles of the quantum mechanical concepts of waves, particles and wave packets.
2. Explain the limits of classical physics at the microscopic level.
3. Describe basic physical systems in terms of Schrodinger's equation.
4. Analyse problems in quantum mechanics at the microscopic level.
5. Solve simple numerical problems in quantum mechanics at the microscopic level.

This Year 2, 10-credit module introduces the standard approach to Quantum Physics. The concept of the wavefunction is introduced together with the time-dependent and the time-independent Schrödinger Equation, and the Uncertainty Principle. We introduce the formalism of quantum mechanics starting with spin-half systems, and generalizing to the basic postulates.

The particle in a box problem is solved in detail, and a description of the harmonic oscillator and central potential (hydrogen atom) is introduced.

Limits of classical physics: black body radiation, photo-electric effect. Recap of wave-particle duality. De Broglie relationships. Hamiltonian mechanics and Poisson brackets.

Wavefunction and its interpretation. Time-dependent and time-independent Schrödinger equations.

Operators, eigenvalues, eigenvectors and possible results of a measurement. Expectation values.
Solution of the Schrödinger equation for an infinite well.
Degeneracy. Correspondence Principle. Symmetric and anti-symmetric solution.

The Schrödinger Equation for the harmonic oscillator Zero-point energy. Heisenberg Uncertainty Principle. Energy spectrum of the harmonic oscillator.
Introduction to the energy spectrum of the hydrogen atom and good quantum numbers.

Scattering
Scattering by a finite well, Tunnelling

This module is at CQFW Level 5