Abstract
A mixed supersymmetric-algebraic approach is employed to generate the minimum uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators. The method proposed produces the superpotentials, ground state eigenfunctions and associated eigenvalues as well as the Schrödinger equation in the factorized form amenable to direct treatment in the algebraic or supersymmetric scheme. In the standard approach the superpotentials are calculated by solution of the Riccati equation for the given form of potential energy function or by differentiation of the ground state eigenfunction. The procedure applied is general and permits derivation the exact analytical solutions and coherent states for the most important model oscillators employed in molecular quantum chemistry, coherent spectroscopy (femtochemistry) and coherent nonlinear optics.
Highlights
The coherent states discovered by Schrödinger in 1926 [1] are usually defined in the following manner [2]: (1) they are eigenstates of the annihilation operator, (2) they minimize the generalized position-momentum uncertainty relation and (3) they arise from the operation of a unitary displacement operator to the ground state of the oscillator
We extend the research area to construct the minimum-uncertainty coherent states of the hyperbolic Rosen–Morse (HRM) [16] and trigonometric Rosen–Morse (TRM) oscillators [17]
The minimum-uncertainty coherent states of the HRM and TRM oscillators have been obtained within the mixed supersymmetric-algebraic method, which permits generating the coherent states of the well-known anharmonic oscillators and deriving superpotentials without necessity of using the ground-state wave function or solving the Riccati equation for a given form of the potential energy function
Summary
The coherent states discovered by Schrödinger in 1926 [1] are usually defined in the following manner [2]: (1) they are eigenstates of the annihilation operator, (2) they minimize the generalized position-momentum uncertainty relation and (3) they arise from the operation of a unitary displacement operator to the ground state of the oscillator. We extend the research area to construct the minimum-uncertainty coherent states of the hyperbolic Rosen–Morse (HRM) [16] and trigonometric Rosen–Morse (TRM) oscillators [17]. Those models are widely used in many areas of exact sciences including quantum chromodynamics (quark interactions) [18], N-fold supersymmetries in Schrödinger, Pauli and Dirac equations [19], SUSYQM [17, 20], the theory of molecular vibrations [16, 21] and other fields of modern chemistry [22, 23] and physics [24]. We shall be concerned with obtaining exact analytical solutions and coherent states for the rotating TRM oscillator with possible application in generating coherent states of the hydrogen atom in the expanding universe or the strong interactions of quarks—the fundammental constituent of hadrons
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