Exact Solution of the Schr\"odinger Equation for Complex Mass Quantum System under Complex Morse Potential to Study Emergent Matter Types
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 classes of non-Hermitian quantum states. 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 systems 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 matter 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.