Effective numerical algorithm for constructing the Wigner function of a quantum system with a polynomial potential in the phase space
Seminar of the Scientific Department of Computational Physics
Date and Time: Thursday, 1 October 2020, at 11:00 AM
Venue: Online seminar on Webex, Laboratory of Information Technologies
Seminar topic: «Effective numerical algorithm for constructing the Wigner function of a quantum system with a polynomial potential in the phase space»
Authors: E. E. Perepelkinabcd, B. I. Sadovnikovb, N. G. Inozemtsevacd, E. V. Burlakovbd, R. V. Polyakovaa
a – Joint Institute for Nuclear Research
b – Lomonosov Moscow State University
c – Dubna State University
d – Moscow Technical University of Communications and Informatics
Speaker: E. V. Burlakov
When considering quantum systems in the phase space, the Wigner function is used as a function of the quasi-probability density. Finding the Wigner function is related to the calculation of the Fourier transform of a certain composition of wave functions of the corresponding quantum system. As a rule, the knowledge of the Wigner function is not the ultimate goal, and computations of the average values of different quantum characteristics of a system are required.
An explicit solution of the Schrödinger equation can be obtained only for a narrow class of potentials; therefore, numerical methods to find wave functions are used in most cases. Consequently, finding the Wigner function is associated with the numerical integration of grid wave functions. When considering a one-dimensional system, it is obligatory to calculate N2 Fourier integrals of the grid wave function. To provide the required accuracy for the wave functions corresponding to the higher states of a quantum system, a larger number of grid nodes is needed.
The goal of the given work was to construct a numerical-analytical method for finding the Wigner function, which would significantly reduce the number of computational operations. Quantum systems with polynomial potentials, for which the Wigner function is represented as a series in some known functions, was considered. The work was supported by the RFBR grant No. 18-29-10014.