https://doi.org/10.1140/epjp/s13360-025-06453-3
Regular Article
Hidden bound states and Shannon information entropies of quasi-exactly solvable quantum oscillators in curved space
1
Department of Mathematics, Visva-Bharati, 731235, Santiniketan, West Bengal, India
2
Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, 603203, Kattankulathur, Tamil Nadu, India
Received:
26
March
2025
Accepted:
19
May
2025
Published online:
26
June
2025
In this work, an approximation scheme based on double-exponential finite Whittaker Cardinal function has been developed for obtaining bound-state spectra and position space Shannon information entropies of nonrelativistic quantum mechanical models in curved space. The reduced radial part of the Schrödinger equation, initially defined in a finite domain 
, is converted into a Sturm–Liouville problem in 
, which is subsequently transformed into a matrix eigenvalue problem in 
by the approximation of the unknown eigenfunctions on the basis of a Paley–Wiener space of finite bandwidth. To examine the efficiency and reliability of the proposed scheme, it has been first applied to the exactly solvable nonlinear harmonic oscillator problem in curved space to approximately evaluate the energy spectrum and position space Shannon information entropies and found highly accurate. These observations encouraged us to apply this scheme to recover available exact states and divulge hidden states for quasi-exactly solvable polynomial and rational extensions of the nonlinear harmonic oscillator problems and subsequently evaluate the corresponding Shannon information entropies in configuration space. Judicious analysis of the results of the examples exercised here reveals that the proposed scheme is a reliable and efficient tool for obtaining several physical quantities depending on bound-state eigenspectra in the studies of cosmological problems (e.g., quasinormal modes of black holes and black branes).
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
