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PH30030: Quantum mechanics

Follow this link for further information on academic years Academic Year: 2020/1
Further information on owning departmentsOwning Department/School: Department of Physics
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Honours (FHEQ level 6)
Further information on teaching periods Period: Semester 1
Further information on unit assessment Assessment: EX 100%
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites 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}
Further information on descriptions 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.
Further information on programme availabilityProgramme availability:
NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2020

PH30030 is Compulsory on the following programmes:

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

Notes: