Ladder operators and coherent states for the Rosen–Morse system and its rational extensions

Abstract

Ladder operators for the hyperbolic Rosen–Morse (RMII) potential are realized using the shape invariance property appearing, in particular, using supersymmetric quantum mechanics. The extension of the ladder operators to a specific class of rational extensions of the RMII potential is presented and discussed. Coherent states are then constructed as almost eigenstates of the lowering operators. Some properties are analyzed and compared. The ladder operators and coherent states constructions presented are extended to the case of the trigonometric Rosen–Morse (RMI) potential using a point canonical transformation.

Confinement in bilayer graphene via intra- and inter-layer interactions

“…which corresponds to the Morse-Rosen interaction [30] (also known as the hyperbolic Rosen-Morse potential), one of the well-known exactly solvable models in quantum mechanics [28,[31][32][33]. Interestingly, for = 1, the potential (43) reduces to the Pöschl-Teller interaction, a particular case to be discussed in detail in the upcoming sections.…”

Linking ladder operators for the Rosen-Morse and Pöschl-Teller systems

“…However, more elaborated one-dimensional exactly solvable systems like the Rosen-Morse system fall outside the range of application of this algebraic method. This system, originally introduced as a model to study vibrations of polyatomic molecules, has been studied in different contexts recently [3][4][5][6]. Indeed, two different ladder operators realizations have been proposed in the literature, both as higher-order differential operators [4,5].…”

“…This system, originally introduced as a model to study vibrations of polyatomic molecules, has been studied in different contexts recently [3][4][5][6]. Indeed, two different ladder operators realizations have been proposed in the literature, both as higher-order differential operators [4,5]. The first of which was motivated by an analogy with classical mechanics [6]; while the second arises purely from quantum mechanics through the concept of shape invariance in supersymmetric quantum mechanics (SUSYQM) [7].…”

Linearised coherent states for non-rational SUSY extensions of the harmonic oscillator

“…Later on, in 1962, Glauber rediscovered these states, known as coherent states, and found that they provided the quantum description of coherent light [13]. Since then, there has been a continuous research activity in quantum physics looking for quantum states with a behaviour at the border between classical and quantum regimes by examining semi-classical phase-space properties, in particular, by systems generated by SUSY [4,[14][15][16][17][18][19][20].…”