https://doi.org/10.1140/epjp/s13360-023-04042-w
Regular Article
An extension of quantum Hamilton-Jacobi formalism to N-spatial dimensions and its applications
1
Department of Physics, Erciyes University, 38039, Kayseri, Turkey
2
Department of Natural and Mathematical Sciences, Tarsus University, 33400, Mersin, Turkey
Received:
1
February
2023
Accepted:
24
April
2023
Published online:
25
May
2023
Due to the importance of hyperspherical coordinates, we report the quantum Hamilton-Jacobi formalism in N
2 spatial dimensions. The quantum momentum function equations in N-dimensions have been constructed within the framework of non-relativistic theory. We also study the singularity structure of the quantum momentum function, which yields the determination of the bound state spectra of stationary quantum systems. In order to confirm the reliability of quantum Hamilton-Jacobi formalism in N-dimensions, we present the numerical data in support of the theoretical results obtained in the context of non-relativistic domain. We analyze the pole structure of the quantum momentum function for the 
molecule in the ground electronic state interacting with Kratzer oscillator in hyperspherical coordinates. Numerical results reveal clearly that moving poles of the quantum momentum function depend on nodes in the hyperradial wave function of related molecule. We also discuss in detail the influence of dimensions on the quantum momentum function.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
