MPhys Physics with Theoretical Physics / Course details

Introduction to Quantum Mechanics

• Mathematics 2 PHYS10372 OR Introduction to Ordinary Differential Equations MATH11412;
• Vibrations & Waves PHYS10302;
• Quantum Physics and Relativity PHYS10121

The unit aims to introduce the framework of quantum mechanics, starting from discrete quantum systems and spin, their time dependence and the Schrödinger equation for the position representation, with examples from the infinite square well and harmonic oscillator.

On completion successful students will be able to:

1. Understand how quantum states are described by wave functions.
2. Deal with operators and solve eigenvalue problems in quantum mechanics.
3. Solve the Schrodinger equation and describe the properties of the simple harmonic oscillator.
4. Deal with algebra of angular momentum operators and solve the simple eigenvalue problems of an angular momentum in quantum mechanics.
5. Use quantum mechanics to describe the hydrogen atom.
6. Use quantum mechanics to describe the properties of one-electron at

Introduction to Quantum Mechanics

• Linear Algebra for Quantum Mechanics: State vectors, matrix notation, operators, eigenvalues and eigenvectors (matrix representation). 
• Fundamentals of Quantum Mechanics: Stern-Gerlach experiment, measurement (projective), commuting observables, uncertainty principle, entanglement, postulates of quantum mechanics. 
• Quantum Hamiltonians: Energy eigenstates, time evolution in QM. 
• Position representation: position and momentum operators, commutation relations and compatibility of different observables. 
• Time-dependent Schrödinger equation and time evolution, time-independent Schrodinger equation as an eigenvalue problem, particle in a box. 
• The harmonic oscillator: Stationary states, energy levels of simple harmonic oscillator, creation and annihilation operators. 
• Time-independent perturbation theory (1st order and 2nd order, including state vector corrections). Application to two-state systems and the harmonic oscillator.
• Barriers and tunnelling, WKB approximation.

10% Tutorial Work/attendance 

Feedback will be offered by tutors on students’ written solutions to weekly example sheets, and model answers will be issued.

A first introduction to quantum physics, Kok, Pieter

Quantum mechanics, Rae, Alastair I. M.

The physics of quantum mechanics, Binney, James

Quantum Mechanics, Mandl, Franz

A modern approach to quantum mechanics, Townsend, John S.

Mathematical methods in the physical sciences, Boas, Mary L.

Mathematics for physicists, Dennery, Philippe.

The principles of quantum mechanics, Dirac, P. A. M.

Quantum computation and quantum information, Nielsen, Michael A.