CODE  PHY2140  
TITLE  Quantum Mechanics  
LEVEL  02  Years 2, 3 in Modular Undergraduate Course  
ECTS CREDITS  6  
DEPARTMENT  Physics  
DESCRIPTION  This studyunit introduces physics students to quantum mechanics. It introduces the basic concepts of quantum mechanics, and focuses on Dirac notation, operator methods, and mixed quantum states. The studyunit will begin with an exploration of the SternGerlach experiment, which will be used to introduce the concept of Dirac notation. The time evolution of quantum systems will be investigated, leading to a discussion of the Schrödinger and Heisenberg pictures. Some properties and implications of the wavefunction will be discussed, including reflection and transmission through a barrier, quantum tunnelling, the notion of the probability current, and the continuity equation. The rate of change of expectation values with time and the Ehrenfest theorem will be derived. The quantum harmonic oscillator will be used as a concrete example of several of these concepts. The theory of angular momentum, and the corresponding operators, will be discussed and used to introduce the abstract concept of spin. Density matrices will be introduced with an emphasis on their connection with, and differences from, pure quantum states. The concepts of measurement and quantum correlations will be introduced through a discussion of Bell's inequality and its relation with the EPR paradox. An exploration of timeindependent perturbation theory will see the studyunit going beyond exactlysolvable problems. Finally, the theory of open quantum systems will be briefly introduced towards the end of the course, providing a connection to realworld situations. Studyunit Aims: This studyunit will provide students with a comprehensive introduction to the concepts and main mathematical tools used in modern quantum mechanics. It will put them in a better position to appreciate recent advances in the field as well as some of the many outstanding issues in quantum mechanics. Learning Outcomes: 1. Knowledge & Understanding By the end of the studyunit the student will be able to:  describe and analyse the SternGerlach experiment;  explain Dirac notation and its use in solving quantum mechanics problems;  calculate the time evolution of states of a simple quantum system starting from its Hamiltonian;  describe how the HamiltonJacobi equation relates to the classical limit of quantum mechanics;  describe the assumptions underlying Bell's inequality, and explain why quantum mechanics violates it;  compare situations that require pure states versus those calling for mixed states;  describe how timeindependent perturbation theory can be used to find approximate results in complex potentials;  explain the major differences between closed and open quantum systems. 2. Skills By the end of the studyunit the student will be able to:  use Dirac notation to solve quantum mechanics problems involving the evolution of systems governed by simple Hamiltonians and ones undergoing measurements;  use operator methods to transform to the interaction picture and to solve quantum mechanics problems;  analyse the quantum harmonic oscillator, and calculate statistical properties (e.g., means and variances) related the states of such a system;  derive the HamiltonJacobi equation and use it to obtain an approximate (WKB) solution to particles in particular potentials;  use timeindependent perturbation theory to calculate modifications of wave functions and eigenenergies in simple situations;  calculate the evolution of mixed quantum states for simple open quantum systems. Main Text/s and any supplementary readings: Main  J J Sakurai, "Modern Quantum Mechanics" (AddisonWesley); chs. 1 to 5 Supplementary  N Zettili, "Quantum Mechanics: Concepts and Applications" (John Wiley & Sons)  J Townsend, "A Modern Approach to Quantum Mechanics" (University Science Books) 

ADDITIONAL NOTES  PreRequisite qualifications: A basic knowledge of calculus and linear algebra  
STUDYUNIT TYPE  Lecture  
METHOD OF ASSESSMENT 


LECTURER/S  Andre Xuereb 

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The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the studyunit description above applies to the academic year 2019/0, if studyunit is available during this academic year, and may be subject to change in subsequent years. 