PH32013: Advanced quantum mechanics
[Page last updated: 23 April 2025]
| Academic Year: | 2025/26 |
| Owning Department/School: | Department of Physics |
| Credits: | 5 [equivalent to 10 CATS credits] |
| Notional Study Hours: | 100 |
| Level: | Honours (FHEQ level 6) |
| Period: |
- Semester 1
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| Assessment Summary: | EXCB 100% |
| Assessment Detail: |
- Written examination (EXCB 100%)
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| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before taking this module you must ( take PH22006 AND take AT LEAST 1 MODULE FROM {PH22010, MA22020} ) OR ( take AT LEAST 1 MODULE FROM {PH20013, PH20060} AND take AT LEAST 1 MODULE FROM {PH20107, MA20219} AND take AT LEAST 1 MODULE FROM {PH20107, MA20223} )
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| 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芒锟斤拷s Golden Rule;
derive and explain the significance of exact solutions of quantum systems;
derive and interpret solutions of the Dirac equation.
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| 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.
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| 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.
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| Course availability: |
PH32013 is Compulsory on the following courses:
Department of Chemistry
- USSC-AAB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 4)
- USSC-AKB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Year long work placement (Year 4)
- USSC-AAM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
- USSC-AAM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
- USSC-AKM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Professional Placement (Year 4)
- USSC-AFM10 : MSci(Hons) Natural Sciences (Physics with Biology) (Year 3)
- USSC-AAM01 : MSci(Hons) Natural Sciences (Physics with Biology stream) with Study year abroad (Year 4)
- USSC-AKM01 : MSci(Hons) Natural Sciences (Physics with Biology stream) with Professional Placement (Year 4)
- USSC-AFM10 : MSci(Hons) Natural Sciences (Physics with Chemistry) (Year 3)
- USSC-AAM01 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 4)
- USSC-AKM01 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) with Professional Placement (Year 4)
Department of Physics
- USPH-AFB24 : BSc(Hons) Physics with Theoretical Physics (Year 3)
- USPH-AAB16 : BSc(Hons) Physics with Theoretical Physics with Study year abroad (Year 4)
- USPH-AKB16 : BSc(Hons) Physics with Theoretical Physics with Year long work placement (Year 4)
- USPH-AFM20 : MPhys(Hons) Physics (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-AFM22 : MPhys(Hons) Physics with Astrophysics (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-AFM23 : MPhys(Hons) Physics with Astrophysics with research placement (Year 3)
- USPH-AAM15 : MPhys(Hons) Physics with Astrophysics with Study year abroad and Research Placement (Year 4)
- USPH-AFM21 : MPhys(Hons) Physics with research placement (Year 3)
- USPH-AAM13 : MPhys(Hons) Physics with Study year abroad and Research Placement (Year 4)
- USPH-AFM24 : MPhys(Hons) Physics with Theoretical Physics (Year 3)
- USPH-AAM16 : MPhys(Hons) Physics with Theoretical Physics with Study year abroad (Year 4)
- USPH-AKM16 : MPhys(Hons) Physics with Theoretical Physics with Professional Placement (Year 4)
- USPH-AKM17 : MPhys(Hons) Physics with Theoretical Physics with Professional and Research Placements (Year 4)
- USPH-AFM25 : MPhys(Hons) Physics with Theoretical Physics with research placement (Year 3)
- USPH-AAM17 : MPhys(Hons) Physics with Theoretical Physics with Study year abroad and Research Placement (Year 4)
- USPH-AFM26 : MSci(Hons) Mathematics and Physics (Year 3)
- USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 4)
- USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 4)
PH32013 is Optional on the following courses:
Department of Chemistry
- USSC-AFB10 : BSc(Hons) Natural Sciences (Biology with Physics) (Year 3)
- USSC-AFB10 : BSc(Hons) Natural Sciences (Chemistry with Physics) (Year 3)
- USSC-AKB01 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Year long work placement (Year 4)
- USSC-AFB10 : BSc(Hons) Natural Sciences (Physics with Biology) (Year 3)
- USSC-AFB10 : BSc(Hons) Natural Sciences (Physics with Chemistry) (Year 3)
- USSC-AAB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 4)
- USSC-AKB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Year long work placement (Year 4)
- USSC-AFM10 : MSci(Hons) Natural Sciences (Biology with Physics) (Year 3)
- USSC-AAM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
- USSC-AFM10 : MSci(Hons) Natural Sciences (Chemistry with Physics) (Year 3)
- USSC-AAM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
- USSC-AKM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Professional Placement (Year 4)
Department of Physics
- USPH-AFB26 : 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-AFB20 : 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-AFB22 : 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)
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Notes: - This unit catalogue is applicable for the 2025/26 academic year only. Students continuing their studies into 2026/27 and beyond should not assume that this unit will be available in future years in the format displayed here for 2025/26.
- 好色tv 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.
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