Quantum information entropies for an asymmetric trigonometric Rosen–Morse potential

Abstract

Shannon entropy for the position and momentum eigenstates of an asymmetric trigonometric Rosen-Morse potential for the ground and first excited states is evaluated. The position and momentum information entropies S x and S p are calculated numerically. Also, it is found that S 1 x is obtained analytically and increases with the potential depth and width. Some interesting features of the information entropy densities ρ s (x) and ρ s ( p) are demonstrated graphically. The Bialynicki-Birula-Mycielski inequality is also tested and found to hold good.

Shannon information entropy for an infinite circular well

“…Once again we find that the S r is almost independent of the quantum number m and S p increases with the quantum number n. This new kind of phenomenon has not been appeared in our previous study [21][22][23][24][25][26]. Certainly, their sum stays above the stipulated lower bound of the value 2(1 + ln π).…”

“…In general, explicit derivations of the information entropy are quite difficult, in particular the derivation of analytical expression for the S p is almost impossible as shown in our recent studies [21][22][23][24][25][26]. Due to the complication of the special function J m involved in the integrals, we cannot obtain their analytical formulas.…”

“…This stimulates us to solve those untouched but interesting quantum systems due to their applications in physics. Therefore, we have studied the quantum information entropies for the symmetrically and asymmetrically trigonometric Rosen-Morse [21,22], the PT-like potential [23], a squared tangent potential [24], the position-dependent mass Schrödinger equation with the null potential [25] and hyperbolic potential [26]. It should be pointed out that most of the contributions mentioned above are concerned with the unconfined quantum systems.…”

Shannon entropy and Fisher information for screened Kratzer potential

“…Many authors have investigated the quantum information for harmonic oscillators in one, two, and three dimensions [ 35,36 ] ; a single‐particle system with central potentials [ 11 ] ; and the shape and effect for quantum heterostructures, [ 37 ] pseudoharmonic potential, [ 38 ] hyperbolic well, [ 39 ] Tangent well, [ 40 ] Kratzer potential, [ 41 ] and many other potential models. [ 14,35,37,42–48 ] So far, exponential‐type potential models are yet to be explored extensively and, as such, are our motivation in the present paper. To the best of our knowledge, the screened Kratzer potential (SKP) model is yet to be studied for quantum information theoretic measures.…”

Information theoretical measures from cumulative and survival densities in quantum systems

“…Since its introduction in 1948, the Shannon entropy of information theory has seen application in a wide variety of fields. The Shannon entropy is a measure of the uncertainty in the underlying distribution, and in recent years there has been an increased interest and application of information theoretical ideas to study problems in electronic structure and quantum theory …”