SubjectsSubjects(version: 875)
Course, academic year 2020/2021
  
Quantum scattering theory - NTMF030
Title: Kvantová teorie rozptylu
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:3/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Additional information: http://utf.mff.cuni.cz/~cizek/atomfyz/TeorieRozptylu.htm
Guarantor: doc. RNDr. Martin Čížek, Ph.D.
Mgr. Roman Čurík, Ph.D.
doc. RNDr. Karel Houfek, Ph.D.
Classification: Physics > Theoretical and Math. Physics
Comes under: Doporučené přednášky 1/2
Annotation -
Last update: T_UTF (29.04.2016)
Introduction to formal non-relativistic quantum scattering theory. Analytic properties of scattering quantities. Solved problems in scattering theory and basics of numerical solution of scattering problems. For the graduate students of the theoretical physics, mathematical modelling and chemical physics.
Course completion requirements - Czech
Last update: doc. RNDr. Karel Houfek, Ph.D. (11.06.2019)

Ústní zkouška a udělení zápočtu, který student dostane za vypracovanání úlohy zadané v poslední třetině semestru.

Literature -
Last update: T_UTF (16.05.2012)

Taylor J. R.: Scattering Theory: The Quantum Theory of Nonrelativistic Collisions, Dover 2006

Friedrich H.: Theoretical Atomic Physics, Springer Verlag, Heidelberg 1991

Kukulin V.I., Krasnopolsky V.M., Horáček J.: Theory of Resonances, Kluwer-Academia, Praha 1989

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

Oral exam. Before coming to exam, student must solve theoretical excercise which will be given to all students in the middle of semester. Oral exam consists of two questions. First question is to explain in detail the theoretical background of the solution of the excercise. The second question will be selected from the topics covered by sylabus of the lecture.

Syllabus -
Last update: Mgr. Zdeněk Mašín, Ph.D. (23.09.2019)

I. INTRODUCTION TO CLASSICAL SCATTERING THEORY:

Trajectory, asymptote. Deflection function, differential cross section.

EXAMPLES: Hard sphere. Typical interatomic potential: rainbow, glory and orbiting phenomena.

II. GENERAL FORMULATION OF QUANTUM SCATTERING THEORY:

Separation of free and non-free dynamics. Trajectory, asymptote. Asymptotic condition and Moller operator. Orthogonality, asymptotic completeness, S-operator. Properties of S-operator, energy conservation, optical theorem. Differential cross section.

III. TIME INDEPENDENT FORMULATION:

Green’s operator and resolvent and their properties. Lippmann-Schwinger equation for stationary states and T-operator. Asymptotics of stationary scattering solution in different bases: K-matrix, T-matrix, S-matrix.

IV. SCATTERING FROM SPHERICALLY SYMMETRIC POTENTIAL:

Angular momentum conservation for scattering quantities. Scattering phase shift. Partial scattering amplitude and partial wave expansion of cross section. Expansion of the Green’s function and stationary states.

EXAMPLES: Practical applications. Numerical implementation of a method for solving radial Schrödinger equation. Application to electron scattering from atom.

V. ANALYTICITY IN p AND E

Transformation of L-S equation to equation of Voltera type. Jost function and Jost solution and their properties. Interpretation of S-matrix poles. Levinson’s theorem.

VI. ANALYTIC PROPERTIES NEAR E -> 0 AND NEAR A RESONANCE.

Scattering length and its behavior. Resonance. Phaseshift behavior. Breit-Wigner and Fano formula.

VII. INTRODUCTION TO MULTICHANNEL SCATTERING

Channels, channel hamiltonian and interaction. Stationary scattering states and multichannel L-S equation. Method of coupled-channels. Cross sections.

VIII. VARIATIONAL PRINCIPLES IN SCATTERING

Kohn method and its usage in basis. Schwinger variational principle.

IX. R-MATRIX METHOD

Basic principles and derivation of the method. Use of basis. Pole expansion of R-matrix.

X. PARTIAL WAVE METHOD

Application to nonspherical and nonlocal potentials. Boundary conditions and cross sections.

XI. INTRODUCTION TO QUANTUM DEFECT THEORY

Rydberg states and quantum defect. Threshod behavior and Seaton's theorem.

 
Charles University | Information system of Charles University | http://www.cuni.cz/UKEN-329.html