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Course, academic year 2019/2020
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Quantum Mechanics I - NTMF066
Title in English: Kvantová mechanika I
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: winter
E-Credits: 9
Hours per week, examination: winter s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Martin Čížek, Ph.D.
Incompatibility : NBCM110, NFPL010, NJSF060, NJSF094, NOFY042, NOFY045
Interchangeability : NJSF094
Is incompatible with: NBCM110, NJSF094
Is interchangeable with: NJSF094
Annotation -
Last update: T_UTF (14.05.2010)
More advanced course of nonrelativistic quantum theory in the extent of state examination in theoretical physics. Basic concepts of the quantum theory. Simple solvable models. Quantum dynamics. Approximation methods. Basics of nonrelativistic scattering theory. Particles in Coulomb field.
Literature - Czech
Last update: T_UTF (14.05.2010)

J. Formánek: Úvod do kvantové teorie (Academia, Praha, 1983, 2004)

Cohen-Tannoudji, Diu, Laloe: Quantum Mechanics (Wiley 2006)

L.D. Landau, E.M. Lifshitz: Quantum Mechanics Non-Relativistic Theory (Butterworth-Heinemann, 1981)

J.J. Sakurai: Modern Quantum Mechanics (Addison-Wesley, Reading, 1985, 1994)

L.E. Ballantine: Quantum Mechanics. A Modern Development (World Scientific, Singapore, 1998)

R.H. Landau: Quantum Mechanics II (Wiley 1996)

Requirements to the exam -
Last update: doc. RNDr. Martin Čížek, Ph.D. (16.10.2017)

Exam constist of written and oral part. To access the exam student must gain enough point from home excercises and test. In the case of excelent results in home excercises and test the written part of exam can be skipped. In oral exam student demonstrates the understanding of theory in two topics selected form the sylabus.

Syllabus -
Last update: T_UTF (14.05.2010)

Basic concepts of quantum theory. State space, operators, measurement. Composite systems.

Operators of basic measurable quantities. Spectral decomposition. Energy and momentum. Stationary states. Basics of representation theory, unitary transformations. Angular momentum.

Simple solvable models. Particle in spherical potential, linear harmonic oscillator, particle in lattice.

Quantum dynamics. Schrödinger equation. Schrödinger, Heisenberg and interaction (Dirac) representation. Green's functions. Classical limit of quantum theory, correspondence principle.

Approximation methods I: variational principle, perturbation expansions, WKB approximation.

Basics of nonrelativistic scattering theory. Time dependent/independent formulation. Variational formulation. S and T matrix. Optical theorem. Born approximation. Limits of low and high energies. Partial wave expansion, phase shifts.

Resonances.

Particle in Coulomb field. Bound states and scattering.

 
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