Position- and Momentum-Space Quantum Information Measures of the Double-Morse Oscillator

This paper investigates the quantum-information properties of a particle confined within a double-Morse potential. The authors utilize the quasi-exact solvability of the system to derive analytical expressions for the first two bound states (ground and first excited). By varying a dimensionless parameter A, which controls the transition from a well-separated double-well potential to a merged single-well profile, the authors compute several information-theoretic measures: Shannon entropy, Onicescu energy, Fisher information, statistical complexity, and Fisher-Shannon products in both position and momentum spaces.

The study reveals that the double-well geometry significantly influences the distribution of information. When the double-well character is pronounced (small A), the position distribution is delocalized across both wells, leading to higher position entropy and lower momentum entropy. As the wells merge (A approaching 1), the particle localizes near the center, which decreases position entropy and increases momentum entropy. The authors find that the ground-state Fisher-Shannon product approaches its Gaussian reference value in the single-well limit, signaling a transition toward Gaussian-like behavior. In contrast, the excited state retains a stronger non-Gaussian structure throughout the transition, evidenced by its persistent nodal profile and higher statistical complexity.

These findings provide a systematic diagnostic for understanding how quantum systems respond to changes in potential geometry. By connecting information-theoretic measures to physical parameters like barrier height and well separation, the paper offers a framework for characterizing quantum states in various experimental platforms, including ultracold atoms, trapped ions, and proton-transfer systems. The results highlight how global and local information measures can serve as sensitive probes for structural complexity and non-Gaussianity in tunable quantum oscillators.