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## PH30030: Quantum mechanics

Owning Department/School: Department of Physics
Credits: 6
Level: Honours (FHEQ level 6)
Period: Semester 1
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment: Mandatory extra work (where allowed by programme regulations)
Requisites: Before taking this module you must ( take PH20013 OR take PH20060 ) AND take PH20019 AND take PH20020
Description: Aims:
The aim of this unit is to show how quantum theory can be developed from a few basic postulates and how this leads to an understanding of a wide variety of physical phenomena. The unit builds on unit PH20013/60 by providing a more formal and mathematical approach to quantum mechanics.

Learning Outcomes:
After taking this unit the student should be able to:
* explain the relation between wave functions, operators and experimental observables;
* use wavefunction, Dirac and matrix representations of quantum mechanics;
* set up the Schrödinger equation for model systems;
* derive eigenstates of energy, momentum and angular momentum;
* apply approximate methods to more complex systems.

Skills:
Numeracy T/F A, Problem Solving T/F A.

Content:
Concepts and postulates of quantum mechanics (8 hours): The wavefunction and its interpretation. Observables and operators: position, momentum, energy operators. Properties of Hermitian operators: real eigenvalues, orthogonal eigenfunctions, expansion in a complete set of eigenfunctions. Measurements of a quantum system, collapse of the wavefunction. Probabilities of measurements, expectation values. Compatible observables, commutators, the uncertainty principle. Time evolution of the wavefunction, time dependent SchrÃ¶dinger equation. Stationary states, time independent Schrödinger equation. Spreading of a Gaussian wavepacket. Dirac notation. Matrix representation of quantum mechanics.
Angular momentum (4 hours): Definitions, operators and commutators. Ladder operators. Eigenvalues and eigenfunctions, spherical harmonics. Spin angular momentum, Pauli spin matrices.
Solutions of the Schrödinger equation in 3D (3 hours): Separation in Cartesian and spherical polar coordinates. Examples, including the hydrogen atom.
Approximate methods (5 hours): Stationary states: non-degenerate and degenerate perturbation theory. Examples. Time-dependent perturbation theory: Fermi’s golden rule, atomic transitions, selection rules.
Identical particles (2 hours): Symmetry relations for bosons and fermions. Pauli exclusion principle.
Programme availability:

#### PH30030 is Compulsory on the following programmes:

Department of Physics
• USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 4)
• USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
• USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)
• USPH-AFM02 : MPhys(Hons) Physics (Year 3)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 4)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 4)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 3)

#### PH30030 is Optional on the following programmes:

Programmes in Natural Sciences
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences with Year long work placement (Year 4)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Year 3)
• UXXX-AKM02 : MSci(Hons) Natural Sciences with Professional Placement (Year 4)
• UXXX-AAM02 : MSci(Hons) Natural Sciences with Study year abroad (Year 4)
Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
Department of Physics
• USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
• USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
• USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
• USPH-AFB01 : BSc(Hons) Physics (Year 3)
• USPH-AAB02 : BSc(Hons) Physics with Study year abroad (Year 4)
• USPH-AKB02 : BSc(Hons) Physics with Year long work placement (Year 4)
• USPH-AFB09 : BSc Physics (Year 3)
• USPH-AFB05 : BSc(Hons) Physics with Computing (Year 3)
• USPH-AAB06 : BSc(Hons) Physics with Computing with Study year abroad (Year 4)
• USPH-AKB06 : BSc(Hons) Physics with Computing with Year long work placement (Year 4)

Notes:
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.