Morse potential derived from first principles

Abstract

We show that a direct connection can be drawn, based on fundamental quantum principles, between the Morse potential, extensively used as an empirical description for the atomic interaction in diatomic molecules, and the harmonic potential. This is conceptually achieved here through a non-additive translation operator, whose action leads to a perfect equivalence between the quantum harmonic oscillator in deformed space and the quantum Morse oscillator in regular space. In this way, our theoretical approach provides a distinctive first principle rationale for anharmonicity, therefore revealing a possible quantum origin for several related properties as, for example, the dissociation energy of diatomic molecules and the deformation of cubic metals.

4 pages, 1 figure

References in corpus (5)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Thermostatistics of overdamped motion of interacting particles
• Nonlinear Relativistic and Quantum Equations with a Common Type of Solution
• Displacement operator for quantum systems with position-dependent mass
• Revisiting the displacement operator for quantum systems with position-dependent mass

Cited by in corpus (19)

• A position-dependent mass harmonic oscillator and deformed space
• Generalized space and linear momentum operators in quantum mechanics
• $\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
• Quantum Confinement in Nonadditive Space with a Spatially Dependent Effective Mass for Si and Ge Quantum Wells
• Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes
• Deformed Fokker-Planck equation: inhomogeneous medium with a position-dependent mass
• Information-theoretic measures for a position-dependent mass system in an infinite potential well
• Influence of interface potential on the effective mass in Ge nanostructures
• Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass
• Exact solution and coherent states of an asymmetric oscillator with position-dependent mass
• Inter-occurrence times and universal laws in finance, earthquakes and genomes
• Effective Mass Quantum Systems with Displacement Operator: Inverse Square plus Coulomb-like Potential
• Bounce corrections to gravitational lensing, quasinormal spectral stability and gray-body factors of Reissner-Nordström black holes
• Generalized Extended Momentum Operator
• Two dimensional electron gas in a non-Euclidean space
• How cells stay together; a mechanism for maintenance of a robust cluster explored by local and nonlocal continuum models
• Harmonic oscillators from displacement operators and thermodynamics
• Morse potential in relativistic contexts from generalized momentum operator, Pekeris approximation revisited and mapping
• Sub-bosonic (deformed) ladder operators