We show that the three quantum states (Pólya states, the generalized non-classical states related to Hahn polynomials and negative hypergeometric states) introduced recently as intermediates states which interpolate between the binomial states and negative binomial states are essentially identical. By using the Hermitial-phase-operator formalism, the phase properties of the hypergeometric state...

A variational and perturbative treatment is provided for a family of generalized spiked harmonic oscillator Hamiltonians H = − d dx + Bx + A x + λ xα ,where B > 0, A ≥ 0 , and α and λ denote two real positive parameters. The method makes use of the function space spanned by the solutions |n> of Schrödinger’s equation for the potential V (x) = Bx + A x . Compact closed-form expressions are obtai...

This paper deals with regular singular generalized q-hypergeometric equations with either “large” or “small” Galois groups. In particular, we consider the fundamental problem of finding appropriate Galoisian substitutes for the usual notion of local monodromy.

In this work, the canonical transformation method is applied to a general second order differential equation (DE) in order to trasform it into a Schrödinger-like DE. Our proposal is based on an auxiliary function g(x) which determines the transformation needed to find exactly-solvable potentials associated to a known DE. To show the usefulness of the proposed approach, we consider explicitly th...

Abstract The main aim of this article is to study a new generalizations the Gauss hypergeometric matrix and confluent functions by using two-parameter Mittag–Leffler function. In particular, we investigate certain important properties these extended such as integral representations, differentiation formulas, beta transform, Laplace transform. Furthermore, introduce an extension Jacobi orthogona...

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anoma...

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0 F 3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the ano...

A procedure for generating infinite series identities makes use of the generalized method of exhaustion by analytically evaluating the inner series of the resulting double summation. Identities are generated involving both elementary and special functions. Infinite sums of special functions include those of the gamma and polygamma functions, the Hurwitz Zeta function, the polygamma function, th...