Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Student mathematical library

Three-dimensional problems in quantum mechanics. A three-dimensional free particle

L. D. Faddeev, O. Yakubovskiĭ

Published Mar 9, 2009• 0 citations
Publisher
DOI
10.1090/stml/047/21

Related papers

One-dimensional problems of quantum mechanics. A free one-dimensional particle

L. D. Faddeev, O. Yakubovskiĭ

Student mathematical library•Mar 9, 2009•0 citations

A one-dimensional lattice model for a quantum mechanical free particle

A. C. de la Torre, Alejandro Daleo

arXiv:quant-ph/9905031•The European Physical Journal D•Jan 1, 2000•27 citations

On the Time Operator in Quantum Mechanics: Three Typical Examples

Taku Goto, K. Yamaguchi, N. Sudo

The so-called time operator in quantum mechanics which may be regarded as a coordinate conjugate to Hamiltonian operator is studied. Three typical examples of the time operators in one-dimensional problem are explicitly obtained; that is, a free particle, a harmonic oscillator and a particle in a square well potential. Our procedure to construct the time operator seems to be useful in a more general case. Qualitative nature of the time operator may be understood from the three examples.

Progress of Theoretical Physics•Nov 1, 1981•18 citations

Semiclassical study of particle motion in two-dimensional and three-dimensional elliptical boxes. I

Yves Ayant, Robert Arvieu

The authors compare three problems of quantum mechanics (or more generally of wave mechanics) which reduce to the same problem in classical mechanics and which can also be treated semiclassically by the Einstein, Brillouin and Keller (1958) semiquantisation rules. The free particle motion in an ellipsoidal oblate or prolate cavity (a deformed nucleus) is compared to that in a plane elliptical billiard box. Separation of variables is performed in appropriate coordinate systems. The presence of a separatrix in phase space is exhibited, which is connected to a potential barrier that is different for each problem. The uniform approximation is used to calculate WKB phase rules appropriate to each symmetry. An important difference results between the prolate and the oblate systems.

Journal of Physics A Mathematical and General•Feb 1, 1987•25 citations

Finite-dimensional quantum mechanics of a particle

R. Jagannathan, Thalanayar S. Santhanam, Ramabhadra Vasudevan

International Journal of Theoretical Physics•Oct 1, 1981•31 citations

Quantum Mechanics in Three Dimensions

Luis Grave de Peralta, Maricela Fernández Lozada, Hira Farooq +3 more

Undergraduate lecture notes in physics•Jan 1, 2023•0 citations
The authors compare three problems of quantum mechanics (or more generally of wave mechanics) which reduce to the same problem in classical mechanics and which can also be treated semiclassically by the Einstein, Brillouin and Keller (1958) semiquantisation rules. The free particle motion in an ellipsoidal oblate or prolate cavity (a deformed nucleus) is compared to that in a plane elliptical billiard box. Separation of variables is performed in appropriate coordinate systems. The presence of a separatrix in phase space is exhibited, which is connected to a potential barrier that is different for each problem. The uniform approximation is used to calculate WKB phase rules appropriate to each symmetry. An important difference results between the prolate and the oblate systems.