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Valid for year : 2007
 
TF1002 Quantum Mechanics, 7,5 ECTS credits.
/Kvantmekanik I/

For:   COM  

 

Prel. scheduled hours:
Rec. self-study hours: 200

  Area of Education: Natural Sciences

Subject area: Physics
  Advancement level (G1, G2, A): A

Aim:
The course goal is to give an exposition of the basic principles of quantum mechanics and its applications. After completing the course tudents should be able to:
  • know and to use the main postulates and notions of quantum mechanics such as quantization, uncertainty principle, superposition, quantum state space, operators, probability amplitude, entanglement;
  • solve the Schrödinger equation for the cases of a harmonic oscillator, a particle in potentials with discontinuities, a particle in periodical structures and in an electromagnetic fields;
  • know the different formulations of quantum mechanics, especially, wave mechanics and Dirac formulation;
  • know the definition and properties of spin and angular momentum of the particles.


Prerequisites: (valid for students admitted to programmes within which the course is offered)
Modern Physics, Quantum Mechanics

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
Supplementary courses:
Quantum Dynamics
Organisation:
The course contains lectures and solution of home problems.
Course contents:

Introduction to quantum mechanics: wave function and its interpretations, principle of superposition, spreading of wave packets and Heisenberg uncertainty relations.
Principles of wave mechanics: Schröodinger equation, coordinate and momentum spaces, operators and expectation values of dynamical variables, stationary states, Hermitian operators, their eigenfunctions and egeinvalues, unitary operators.
Applications of wave equations: free particle, charged particle in external electromagnetic field, linear harmonic oscillator potential step, rectangular potential barrier and square well potentials, transmission coefficient and resonances. WKB approximation.
Variational methods and perturbation theory: Rayleigh-Ritz method, perturbation theory of Schrödinger equation.
Dirac formulation of quantum mechanics: vector and operators in abstract vector space, eigenvalue problem and measurements of observables, Heisenberg uncertainity principle, quantization. Angular momentum.
Concept of spin: wave mechanics with spin, spinors, Pauli spin operator and Pauli matrices, total angular momentum, Clebsch-Gordan coefficients, spectral line splitting.

Course literature:
E. Merzbacher. Quantum mechanics, 3rd edition, John Wiley and Sons, 1998 (chapter 1-12 and 16).

Examination:
Oral examination, solutions of home problems.
 5 p
/
7,5 ECTS
 


Course language is English.
Department offering the course: IFM.
Director of Studies: Leif Johansson
Examiner: Irina Yakymenko

Course Syllabus in Swedish

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Contact: TFK , val@tfk.liu.se
Last updated: 06/02/2008