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.

Non-Hermitian PT Symmetric Hamiltonian with Position-Dependent Masses: Associated Schrödinger Equation and Finite-Norm Solutions

“…The proposal for an effective mass m e = m/(1 + γ x) 2 , considered in Refs. [14][15][16][17], is expected to be relevant for a some types of np junctions, where a gradual decrease in the concentration of electrons is verified for x > 0. In the present framework, the effective-mass form of (3) is symmetric around its maximum value at x = 0 and decreases for increasing values of |x|, so that m e ∼ |x| −4 , when √ γ x 1.…”

“…This happens to be the case in the proposals of Refs. [9][10][11][12][13][14][15][16][17], which considered linear SEs, but with position-dependent masses. One main motivation concerns a proper description of some semiconductor heterostructures [18,19].…”

Bohmian formalism and Fisher information from q-deformed Schrödinger equation

“…Recently, Costa Filho et al [23,24,25,26] have introduced a generalized translation operator which produces nonadditive spatial displacements, i.e.,…”

Entropy behavior for isolated systems containing bounded and unbounded states: latent heat at the inflection point

“…This work focuses on studying this inflection point for bounded potentials. A common application, Morse's potential is a dressed approximation describing intramolecular interactions that allow for dissociations [8][9][10]. It has been considered widely in treatments of molecular bonds [11,12] and applications of the Fokker-Planck equations for lasers [13].…”

“…Furthermore, the associated spectrum is the union of a finite set of levels and the continuum. The discrete energy spectrum E is [8][9][10]14] = -…”