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August 16, 2025

Exact solution of Schrödinger equation for the complex Morse potential to investigate physical systems with position-dependent complex mass

Key Points

Identifying bounded eigenstates leads to insights about physical systems with complex masses and potentials.
The analysis demonstrates that the derived solutions conform to the requirements of the Schrödinger equation with complex morse potential.
Investigating several scenarios reveals implications of the existing eigenspectrum on physical systems of interest.
This framework supports the development of a quantum mechanical model contributing to our understanding of dark matter.

Abstract

Abstract This paper obtains the exact solution of the ground state of a diatomic particle system with position-dependent complex mass under the action of complex morse potential in the quantum domain. The analyticity condition of the potential parameters and eigenfunction is employed to deduce the eigenfunction and eigenenergy by solving the position-dependent Schr¨odinger equation for the potential mentioned above in the extended complex phase space masses without any assumption of the mass profile The condition for the admittance of the reality of the eigenspectrum is derived and applied to analyze several cases of physical interest. The existence ofbounded eigenstates in several cases of physical interest along with the localized nature of the probability current density function for such physical systems points towards their presence over certain bounded domains. This study also aims to draw parallelsbetween these quantum systems and dark matter, contributing to the development of a viable quantum mechanical model to explain its properties.

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