Quantum Theory of Resonances - NBCM134
Title: Kvantová teorie rezonancí
Guaranteed by: Department of Chemical Physics and Optics (32-KCHFO)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. Mgr. Jaroslav Zamastil, Ph.D.
RNDr. Milan Šindelka, Ph.D.
Teacher(s): RNDr. Milan Šindelka, Ph.D.
Opinion survey results   Examination dates   SS schedule   Noticeboard   
Annotation -
This course is suitable for students who have passed through an introductory quantum mechanics, and who wish to delve deeper into more sophisticated and subtle parts of quantum theory (scattering, nonhermitian formalism, light-matter interaction). The lectures are aimed not only at highlighting fundamental physics insights, but also at introducing a broad range of powerful mathematical and computational techniques. At the end of the course, the students can choose either an open book exam or a final project (which can possibly end up with an original scientific paper).
Last update: Kapsa Vojtěch, RNDr., CSc. (19.02.2018)
Aim of the course -

Introduction to the hermitian and non-hermitian theory of scattering phenomena.

Last update: Kapsa Vojtěch, RNDr., CSc. (28.02.2018)
Literature -

[1] J. R. Taylor: Scattering Theory (The Quantum Theory of Nonrelativistic Collisions), Dover Publications, 2000.

[2] P. Roman: Advanced Quantum Theory, Addison-Wesley, 1965.

[3] N. Moiseyev: Non-Hermitian Quantum Mechanics, Cambridge, 2011.

Last update: Kapsa Vojtěch, RNDr., CSc. (19.02.2018)
Teaching methods -

lectures

Last update: Kapsa Vojtěch, RNDr., CSc. (28.02.2018)
Requirements to the exam -

The students can choose either an oral exam (corresponding to the syllabus and to the contents of the presented lectures) or a written (open book) exam based upon a mini-project related to scattering theory.

Last update: Kapsa Vojtěch, RNDr., CSc. (28.02.2018)
Syllabus -
introduction to scattering theory
  • time dependent picture of scattering, asymptotic condition, in- and out- states, S-matrix, cross sections
  • time independent formalism of scattering theory: Lippmann-Schwinger equation, T-matrix, Green operators, Born series
  • applications: transmission/reflection probabilities for 1D problems, scattering cross sections in 3D
  • scattering resonances: shape, Feshbach, light induced

nonhermitian scattering theory

  • analytic continuation of the S-matrix into the complex energy/momentum plane
  • classification of the poles of the S-matrix: (anti)bound states, (anti)resonances
  • Siegert pseudostate formalism interconnecting the nonhermitian world with the conventional scattering theory
  • application: scattering problems in 1D

complex scaling methods for the calculation of resonances

  • wavefunction of metastable states in the x-representation
  • complex transformations of Hamiltonian as implicated by its Laplace-Fourier representation
  • numerical applications of the complex transformations of the Hamiltonian

atoms in strong electromagnetic field

  • Hamiltonian for laser-matter interaction
  • application of the Floquet theory for the interaction of atoms with electromagnetic field in the classical dipole approximation

incomplete spectrum in the case non-hermitian Hamiltonian

  • exceptional point (branch point)
  • quantum dynamics when encircling an exceptional point
  • PT symmetric waveguides

Last update: Kapsa Vojtěch, RNDr., CSc. (19.02.2018)