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

Abstract

This paper presents the exact ground state solution for a diatomic particle system with position-dependent complex mass under action of a complex Morse potential in the quantum domain. By solving the position-dependent Schrödinger equation in extended complex phase space without assuming a specific mass profile, we derive both the eigenfunctions and corresponding eigenenergies using the analyticity conditions of the eigenfunctions. A key focus is placed on addressing the challenge of normalization inherent in non-Hermitian Hamiltonians. To overcome the limitations of conventional normalization methods in systems with complex potentials and spatially varying mass, we propose a modified normalization approach based on a two-dimensional integral over phase space. The results reveal that, under certain parameter constraints, real energy spectra can arise in non Hermitian settings, supported by normalized and physically meaningful eigenfunctions. Probability density plots validate the existence of stable, localized bound states, maintaining essential characteristics of the traditional Morse potential. Moreover, the model offers potential applications in high-energy and cosmological physics, particularly in the quantum description of exotic systems like dark matter.

arXiv comment24 pages, 16 figures

References in corpus (17)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Effective Mass of One 4he Atom in Liquid 3he
• Solutions of the nonrelativistic wave equation with position-dependent effective mass
• Deformed algebras, position-dependent effective masses and curved spaces: An exactly solvable Coulomb problem
• A quantum exactly solvable non-linear oscillator related with the isotonic oscillator
• A study of the bound states for square potential wells with position-dependent mass
• Morse potential and its relationship with the Coulomb in a position-dependent mass background
• Controlling decoherence via $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian open quantum systems
• The position-dependent matter density probability distribution function
• Antiprotons from Dark Matter: Effects of a Position-Dependent Diffusion Coefficient
• On two superintegrable nonlinear oscillators in N dimensions
• A squeeze-like operator approach to position-dependent mass in quantum mechanics
• Three-dimensional bound states of cylindrical quantum heterostructures with position-dependent mass carriers
• Position-dependent Voronoi probability distribution functions for matter and halos
• Estimation of the Mass of Dark Matter Using the Observed Mass Profiles of Late-Type Galaxies
• Co-interacting dark matter and conformally coupled light scalars