Quantum Theory

Overview

• Overview of classical physics and the need for new theory.
• Basic principles: states and the superposition principle, amplitude and probability, linear operators, observables, commutators, uncertainty principle, time evolution (Schrödinger equation), wavefunctions and coordinate representation.
• Elementary applications: harmonic oscillator, angular momentum, spin.
• Motion in one dimension: free particle, square well, square barrier.
• Approximate methods: semiclassical approximation (Bohr-Sommerfeld quantisation), variational method, time-independent perturbation theory, perturbation theory for degenerate states (example: spin-spin interaction, singlet and triplet states).
• Motion in three dimensions: Schrödinger equation, orbital angular momentum, spherical harmonics, motion in a central field, hydrogen atom.
• Atoms: hydrogen-like systems, Pauli principle, structure of many-electron atoms and the Periodic Table.

Learning Objectives

On the completion of this module, successful students will be able to
• Understand, manipulate and apply the basic principles of Quantum Theory involving states, superpositions, operators and commutators;
• Apply a variety of mathematical methods to solve a range of basic problems in Quantum Theory, including the finding of eigenstates, eigenvalues and wavefunctions;
• Use approximate methods to solve problems in Quantum Theory and identify the range of applicability of these methods;
• Understand the structure and classification of states of the hydrogen atom and explain the basic principles behind the structure of atoms and Periodic Table.

Skills

• Proficiency in quantum mechanics, including its modelling and problem-solving aspects.
• Assimilating abstract ideas.
• Using abstract ideas to formulate specific problems.
• Applying a range of mathematical methods to solving specific problems.

Assessment

None