## PH40084: Advanced quantum theory

[Page last updated: 05 August 2021]

Academic Year: 2021/2
Owning Department/School: Department of Physics
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 2
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take PH30030 OR take PH30043
Aims: The aim of this unit is to increase the breadth and depth of students' knowledge and understanding of quantum physics, in both fundamental aspects of quantum mechanics and modern applications of quantum theory.

Learning Outcomes: After taking this unit the student should be able to:�
* outline clearly� the mathematical foundations and underlying principles of quantum mechanics;
* demonstrate an in-depth understanding of how a quantum description involving many degrees of freedom is described mathematically;
* explain in detail the predictions of relativistic quantum theory: the necessity of spin, the concept of antiparticle, the polarization of the vacuum, spinors, and the fine structure of atoms;
* calculate the effects of magnetic and electric fields on spin ½ particles.

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

Content: Principles of quantum mechanics (7� hours):� Complex vector spaces; Dirac's bra-ket notation; Linear operators; Projectors, positive, hermitian and unitary operators; Postulates of quantum mechanics and quantum measurements; Composite quantum systems and tensor products.

Classical limit of quantum mechanics (2 hours):� Ehrenfest's theorem, limit of ℏ→0�

Relativistic quantum mechanics (10� hours):� Inertia principle and invariance under Lorentz transformation; Klein-Gordon equation; Dirac equation, Dirac sea, Lamb shift; Lorentz transformation of spinors; Plane wave spinors; minimal coupling to electromagnetic fields; Non-relativistic limit of the Dirac equation: origin of the spin and spin-orbit coupling; Atomic fine structure.

Introduction to canonical quantization� (3 hours):� Quantum harmonic oscillator, creation, annihilation and number operators, Fock states, transverse phonons on a periodic chain.

Programme availability:

#### PH40084 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)
Programmes in Natural Sciences
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) (Year 4)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 5)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Professional Placement (Year 5)

#### PH40084 is Optional on the following programmes:

Department of Mathematical Sciences
Department of Physics
• USPH-AFM02 : MPhys(Hons) Physics (Year 4)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 4)
• USPH-AAM03 : MPhys(Hons) Physics with Study year abroad (Year 4)
• USPH-AAM12 : MPhys(Hons) Physics with Study year abroad (Year 5)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 5)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 5)
• USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 4)
• USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 4)
• USPH-AAM10 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 4)
• USPH-AAM14 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 5)
• USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 5)
• USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 5)
• USPH-AAM15 : MPhys(Hons) Physics with Astrophysics with Study year abroad and Research Placement (Year 5)
• USPH-AAM13 : MPhys(Hons) Physics with Study year abroad and Research Placement (Year 5)
Programmes in Natural Sciences
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) (Year 4)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 5)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Professional Placement (Year 5)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Physics with Biology stream) (Year 4)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Physics with Biology stream) with Study year abroad (Year 5)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Physics with Biology stream) with Professional Placement (Year 5)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) (Year 4)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 5)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) with Professional Placement (Year 5)

 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.