Building on the Stage 1 Introduction to Quantum Physics module, Quantum Physics II extends understanding of both quantum mechanics and atomic physics. Through this, concepts of quantization, quantum states, and quantum interactions will be introduced.

## Pre-requisite modules

## Co-requisite modules

## Prohibited combinations

- None

Occurrence | Teaching cycle |
---|---|

A | Autumn Term 2017-18 |

The quantum mechanics component moves on from the initial description in Quantum Physics I, introducing the time dependent Schrödinger equation and the relationship between this and the time-independent Schrödinger equation. Simple 1-, 2- and 3- dimensional physical systems are developed using Schrödinger's equation. It is shown how observable quantities such as position and momentum are represented by Hermitian operators. The properties of these operators are studied. The expansion theorem is introduced and its interpretation in relation to the theory of measurement. The theory is related to observations whenever possible.

The module continues with atomic physics where the principal aim is to impart a basic knowledge of atomic structure, and to illustrate how atomic structure is interpreted from the measurement of spectra. The classical Bohr and Bohr-Sommerfeld theories and semi-classical vector model of atomic structure are applied to the hydrogen atom. The discussion moves to interpretation of the Stern-Gerlach experiment and introduces electron spin and fine structure. Methods for measuring optical spectra, and the observation and interpretation of the Zeeman effect are outlined.

**In Quantum Mechanics, to: **

- Quote and interpret the time-dependent (TDSE) and time-independent (TISE) Schrödinger equations.
- Understand the relationship between the TDSE and the TISE.
- Solve the TISE for simple 1-, 2- and 3-dimensional physical systems, applying appropriate boundary conditions.
- Normalise 1-, 2- and 3-dimensional wave-functions in Cartesian, polar and spherical polar coordinates.
- State the significance and importance of Hermitian operators in representing observable quantities. Be able to quote and apply operators for position, momentum, energy, and angular momentum.
- Prove simple theorems relating to the properties of the eigenfunctions and eigenvalues of Hermitian operators.
- Expand a wave function in terms of a basis set of functions, and interpret the expansion coefficients in terms of measurement probabilities.

**In Atomic Physics, to: **

- Give brief accounts of atomic physics models.
- Define degeneracy, and calculate the degeneracy in atomic systems.
- Describe the origin of optical and X-ray spectral line emission.
- Use and interpret spectroscopic notation.
- Illustrate how spectroscopic measurements are made.
- Construct, label, and compare energy level diagrams.
- Apply the selection rules.
- Perform calculations for simple atomic systems.

*Quantum Mechanics*

- Formal basis of quantum mechanics: the postulates of quantum mechanics; observables, Hermitian operators, and measurements; commutators, compatible observables, and the uncertainty principle.
- Interpretation of the Time-Dependent Schrödinger Equation (TDSE) and solutions of the TDSE using separation of variables.
- Operators and observables: position and momentum operators; the Hamiltonian operator; angular momentum operators; eigenfunctions, eigenvalues, and expectation values.
- The simple harmonic oscillator (SHO); solutions of the TISE; energy eigenvalues and eigenfunctions for the SHO
- Particle in a two- and three-dimensional box and in the three-dimensional harmonic oscillator potential; energy eigenvalues and eigenfunctions; degeneracy table; accidental and symmetry degeneracy.
- Particle in a spherically symmetric potential; the TISE in spherical polar coordinates; the hydrogenic wavefunctions and energy eigenvalues. Eigenfunctions and eigenvalues of the angular momentum operator.

*Atomic Physics*

- Atomic spectra
- Bohr and Bohr-Sommerfeld theories
- The vector model of angular momenta
- Stern-Gerlach experiment and electron spin
- Fine structure
- A summary of the quantum numbers
- One electron atoms and the quantum defect
- Energy diagrams, allowed transitions and selection rules
- X-ray emission and Moseley's Law
- The Zeeman effect

**Lecture notes**

Students are expected to make their own notes from lectures. In addition, handouts are provided covering background material and material that is primarily complicated mathematics which takes time to write on the board and simply help the understanding of the physics.

**Suggested preparation**

The first year lecture material on Quantum Physics is sufficient preparation. The summer preparation material on Mathematics, as well as the booklet “Quantum Mechanics Primer” by Warner & Cheung (available from the Student Administration Office) is highly recommended.

Task | Length | % of module mark |
---|---|---|

Essay/courseworkPhysics Practice Questions |
N/A | 15 |

University - closed examinationQuantum and Atomic Physics |
1.5 hours | 85 |

Non-reassessable

Task | Length | % of module mark |
---|---|---|

University - closed examinationQuantum and Atomic Physics |
1.5 hours | 85 |

Physics Practice Questions (PPQs) - You will receive the marked scripts via your pigeon holes. Feedback solutions will be provided on the VLE or by other equivalent means from your lecturer. As feedback solutions are provided, normally detailed comments will not be written on your returned work, although markers will indicate where you have lost marks or made mistakes. You should use your returned scripts in conjunction with the feedback solutions.

Exams - You will receive the marks for the individual exams from eVision. Detailed model answers will be provided on the intranet. You should discuss your performance with your supervisor.

Advice on academic progress - Individual meetings with supervisor will take place where you can discuss your academic progress in detail.

Rae A I M; *Quantum Mechanics* 4th Ed (McGraw-Hill)*** (*Quantum Mechanics)*

Eisberg R M & Resnick R; *Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles* (Wiley)*** (*Atomic Physics/Quantum Mechanics)*