Dirac approach in review of the classical and quantum motion on the surface of the hyperboloid of one sheet

• Published in: Indian journal of physics Vol. 96; no. 11; pp. 3201 - 3209
• Main Authors: Najafizade, A, Panahi, H, Akbari, S, Jahangiri, L
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 2022; Springer Nature B.V
• Subjects: Astrophysics and Astroparticles; Euclidean geometry; Hyperspaces; Original Paper; Physics; Physics and Astronomy; Schrodinger equation; Dirac bracket; One-sheet hyperboloid; Quantization method
• ISSN: 0973-1458; 0974-9845
• DOI: 10.1007/s12648-021-02250-7

In this article, we study the constrained motion of a free particle on a hyperboloid of revolution of one sheet in the framework of Dirac’s approach as a two-dimensional surface embedded in three-dimensional Euclidean space. We apply this method to determine the Dirac brackets among the variables of the phase space. In the meantime, we briefly present the details of the motion of a particle limited on the one-sheet hyperboloid. Furthermore, using Dirac quantization, we show the appropriate representations for the momentum operators and obtain the Schrödinger equation for presented hypersurface.