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PH30030: Quantum mechanics

[Page last updated: 20 April 2021]

Academic Year: 2021/2
Owning Department/School: Department of Physics
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Honours (FHEQ level 6)
Period:
Semester 1
Assessment Summary: EX 100%
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must ( take PH20013 OR take PH20060 ) AND take AT LEAST 1 AND NO MORE THAN 3 MODULES FROM {PH20019, PH20107, MA20219} AND take AT LEAST 1 AND NO MORE THAN 3 MODULES FROM {PH20020, PH20107, MA20223}
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;
* derive eigenstates of energy, momentum and angular momentum;
* construct operators and apply them to two-particle systems;
* 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 Schrödinger 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.
Many particle systems (5 hours): Systems of two particles. Two distinguishable interacting particles: central potentials, the hydrogen atom. Indistinguishable particles. Symmetric and antisymmetric eigenfunctions: bosons and fermions. Pauli exclusion principle. Triplet and singlet states. Exchange force.
Approximate methods for stationary states (5 hours): Non-degenerate perturbation theory. Degenerate perturbation theory. Variational method - upper bound on ground state energy. Examples.

Programme availability:
NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2021

PH30030 is Compulsory on the following programmes:

Department of Physics
  • USPH-AFM02 : MPhys(Hons) Physics (Year 3)
  • USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 3)
  • USPH-AAM12 : MPhys(Hons) Physics with Study year abroad (Year 4)
  • USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 4)
  • USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 4)
  • USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 3)
  • USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 3)
  • USPH-AAM14 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 4)
  • USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 4)
  • USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 4)
  • USPH-AAM15 : MPhys(Hons) Physics with Astrophysics with Study year abroad and Research Placement (Year 4)
  • USPH-AAM13 : MPhys(Hons) Physics with Study year abroad and Research Placement (Year 4)
  • 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)
Programmes in Natural Sciences
  • UXXX-AFB01 : BSc(Hons) Natural Sciences (Biology with Physics stream) (Year 3)
  • UXXX-AAB02 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
  • UXXX-AKB02 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Year long work placement (Year 4)
  • UXXX-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) (Year 3)
  • UXXX-AAB02 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
  • UXXX-AKB02 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Year long work placement (Year 4)
  • UXXX-AFB01 : BSc(Hons) Natural Sciences (Environmental Science with Physics stream) (Year 3)
  • UXXX-AAB02 : BSc(Hons) Natural Sciences (Environmental Science with Physics stream) with Study year abroad (Year 4)
  • UXXX-AKB02 : BSc(Hons) Natural Sciences (Environmental Science with Physics stream) with Year long work placement (Year 4)
  • UXXX-AFB01 : BSc(Hons) Natural Sciences (Physics with Biology stream) (Year 3)
  • UXXX-AAB02 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Study year abroad (Year 4)
  • UXXX-AKB02 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Year long work placement (Year 4)
  • UXXX-AFB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) (Year 3)
  • UXXX-AAB02 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 4)
  • UXXX-AKB02 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Year long work placement (Year 4)
  • UXXX-AFB01 : BSc(Hons) Natural Sciences (Physics with Environmental Science stream) (Year 3)
  • UXXX-AAB02 : BSc(Hons) Natural Sciences (Physics with Environmental Science stream) with Study year abroad (Year 4)
  • UXXX-AKB02 : BSc(Hons) Natural Sciences (Physics with Environmental Science stream) with Year long work placement (Year 4)
  • UXXX-AFM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) (Year 3)
  • UXXX-AAM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
  • UXXX-AKM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Professional Placement (Year 4)
  • UXXX-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) (Year 3)
  • UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
  • UXXX-AKM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Professional Placement (Year 4)
  • UXXX-AFM01 : MSci(Hons) Natural Sciences (Physics with Biology stream) (Year 3)
  • UXXX-AAM02 : MSci(Hons) Natural Sciences (Physics with Biology stream) with Study year abroad (Year 4)
  • UXXX-AKM02 : MSci(Hons) Natural Sciences (Physics with Biology stream) with Professional Placement (Year 4)
  • UXXX-AFM01 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) (Year 3)
  • UXXX-AAM02 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 4)
  • UXXX-AKM02 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) with Professional Placement (Year 4)

PH30030 is Optional on the following programmes:

Department of Mathematical Sciences
  • 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 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-AFB10 : BSc(Hons) Physics with Astrophysics (Year 3)
  • USPH-AAB10 : BSc(Hons) Physics with Astrophysics with Study year abroad (Year 4)
  • USPH-AKB10 : BSc(Hons) Physics with Astrophysics with Year long work placement (Year 4)

Notes:

  • This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22.
  • Programmes and units are subject to change 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.
  • Find out more about these and other important University terms and conditions here.