- Academic Registry
Course & Unit Catalogues


PH30134: Advanced quantum mechanics

[Page last updated: 09 August 2024]

Academic Year: 2024/25
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: EXOB 100%
Assessment Detail:
  • PH32013 Written examination (EXOB 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}
Learning Outcomes: After taking this unit the student should be able to: construct two- and many-particle wavefunctions of the appropriate symmetry and explain the exchange interaction; apply approximate methods for stationary states; solve time-dependent problems and derive and use Fermi's Golden Rule; derive and explain the significance of exact solutions of quantum systems; derive and interpret solutions of the Dirac equation.


Synopsis: You will further develop your knowledge of the concepts, techniques and applications of quantum mechanics, exploring how many-particle quantum systems are described, using approximation methods to calculate properties of stationary and time-dependent systems, and seeing how the postulates of quantum mechanics and special relativity lead to the Dirac equation and its solutions.

Content: Many particle systems (4 lecture hours): Two particle systems: Distinguishable vs indistinguishable particle systems; symmetric and antisymmetric eigenfunctions: bosons and fermions. Pauli exclusion principle. Triplet and singlet states. Exchange interaction. Many particle systems: Slater determinant wave function. Approximation techniques for stationary states (5 lecture hours): Non-degenerate perturbation theory; degenerate perturbation theory; Variational methods; WKB; Born approximation. Applications. Time-dependent quantum mechanics (5 lecture hours): Time evolution, TDSE, examples (e.g. spin precession). Heisenberg picture/Heisenberg equation of motion. Time-dependent perturbation theory: Fermi's Golden Rule. Exactly soluble problems in quantum mechanics (3 lecture hours): Methods, solution, properties and physical applications of key quantum systems e.g.: 3D harmonic oscillator; charged particles in uniform magnetic field (Landau levels); Aharonov-Bohm effect. Introduction to the Dirac equation (3 lecture hours): Invariance under Lorentz transformation. Dirac equation, Dirac sea. Plane wave spinors; minimal coupling to electromagnetic fields; Non-relativistic limit of the Dirac equation: spin-orbit coupling, atomic fine structure.

Course availability:

PH30134 is Compulsory on the following courses:

Department of Physics
  • USPH-AFB16 : BSc(Hons) Physics with Theoretical Physics (Year 3)
  • USPH-AFM02 : MPhys(Hons) Physics (Year 3)
  • USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 3)
  • USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 3)
  • USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 3)
  • USPH-AFM16 : MPhys(Hons) Physics with Theoretical Physics (Year 3)
  • USPH-AFM17 : MPhys(Hons) Physics with Theoretical Physics with Research placement (Year 3)
  • USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 3)

PH30134 is Optional on the following courses:

Department of Physics

Notes:

  • This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
  • Courses 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.