PH30030: Quantum mechanics
Academic Year:  2020/1 
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:  EX 100% 
Supplementary Assessment: 

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 twoparticle 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): Nondegenerate 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 2020 
PH30030 is Compulsory on the following programmes:Department of Physics
PH30030 is Optional on the following programmes:Department of Mathematical Sciences

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