Open AccessBouncing in an oscillatory gravitational field
Author(s) -
Jérôme Martin,
Paul Strange
Publication year - 2021
Publication title -
european journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.421
H-Index - 51
eISSN - 1361-6404
pISSN - 0143-0807
DOI - 10.1088/1361-6404/abf8c5
Subject(s) - physics , gravitational field , eigenfunction , classical mechanics , observable , field (mathematics) , amplitude , gravitation , equations of motion , motion (physics) , gravitational wave , quantum , theoretical physics , quantum mechanics , eigenvalues and eigenvectors , mathematics , pure mathematics
We apply the time-dependent supersymmetry methods of Bagrov, Samsonov and Shekoyan to the Schrödinger equation for a quantum bouncer. A new family of potentials, that correspond to the linear gravitational potential with a small oscillatory component superimposed upon it, is produced. Both the frequency and amplitude of the oscillatory part can be controlled and the corresponding eigenfunctions are found. These solutions are explored and basic observables are calculated. In particular we examine how motion in such a potential can be distinguished from motion in a linear gravitational field. We also point out some pedagogical aspects of this project.