Singularities of Quantum and Classical Averaging in the Model with Resonance

Student: Belov Dmitrii

Supervisor: Evgeny Vybornyi

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Final Grade: 9

Year of Graduation: 2021

This paper considers a two-dimensional harmonic oscillator with specific perturbation. This work aims to examine the eigenvalues of this system, specifically their numerical and analytical approximations. To this objective, perturbation theory and the averaging method are investigated and Python as a programming language and its libraries for scientific purposes are used. The result of this work is the analytical proof of the degeneracy of eigenvalues of the Hamiltonian.

Full text (added May 31, 2021)

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses