Research Article Orthogonal polynomials attached to coherent states for the symmetric Pöschl–Teller oscillator

ABSTRACT

We consider a one-parameter family of nonlinear coherent states by replacing the factorial in coefficients $z^n/\sqrt{n!}$ of the canonical coherent states by a specific generalized factorial $x_n^{\gamma }!$, $\gamma \ge 0.$ These states are superposition of eigenstates of the Hamiltonian with a symmetric Pöschl–Teller potential depending on a parameter $\nu >1$. The associated Bargmann-type transform is defined for $\gamma =\nu$. Some results on the infinite square well potential are also derived. For some different values of γ, we discuss two sets of orthogonal polynomials that are naturally attached to these coherent states.

KEYWORDS:

• Orthogonal polynomials
• Pöschl–Teller oscillator
• Coherent states
• Bargmann-typetransform

AMS SUBJECT CLASSIFICATION:

• 33C45
• 35A22
• 81R30

Disclosure statement

No potential conflict of interest was reported by the authors.