Exact Solution of Schr\"odinger equation for Complex Mass Quantum System under Complex Morse Potential to study emergent matter types and its phases

TL;DR

This paper derives exact solutions for a non-Hermitian quantum system with complex mass and Morse potential, revealing five matter types and phases, including a dark matter analogue, through spectral and probability analysis.

Contribution

It provides the first exact solutions for complex mass quantum systems with Morse potential, classifies emergent matter types, and explores phase boundaries in a non-Hermitian framework.

Findings

Identification of five intrinsic matter types from spectral analysis

Discovery of a non-dissipative, gravitational-like state as a dark matter analogue

Establishment of conditions for real spectra and physical regimes

Abstract

We present exact solutions of the Schr\"odinger equation for a quantum system with complex mass subjected to a complex Morse potential in the extended complex phase space. The normalized eigenfunctions and corresponding eigenspectra are derived within a non-Hermitian framework, ensuring consistent probability densities. Conditions for the reality of the spectra are established and used to analyze the dependence of eigenvalue behaviour on potential parameters. The study reveals distinct regimes of spectral characteristics arising from the interplay of complex mass, the Morse parameter, and eigenvalues, leading to the emergence of five intrinsic matter types. By analysing the energy eigenspectra, normalization conditions, and probability density profiles across parameter space, we identify regimes corresponding to real-spectrum Hermitian-like matter, quasi-stable or resonant states, purely complex quantum matter, non-physical, non-normalizable states, and a quasi-classical determinate regime in which the probability density becomes spatially static. One of these system exhibits a non-dissipative, collisionless state with long-range gravitational-like characteristics, suggesting a theoretical analogue for dark matter within a non-Hermitian quantum framework. Further, the five identified classes of matter may be interpreted as distinct phases of a single quantum system governed by complex mass and Morse parameters This classification elucidates the boundary between physical and non-physical regimes in complex quantum systems and provides a unified approach for interpreting stability, resonance, and emergent classicality arising from complex parameters.