Quantum-mechanical methods of solving the polyatomic vibrational Schrödinger equation
need higher quality zero-order approximations than ones originating from the harmonic …

Using the analytical transfer matrix method in combination of supersymmetry algebra, we
have analytically derived the eigenenergies of the Morse potential. The derived …

General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements
are derived in Dirac relativistic quantum mechanics. Our approach is based on a …

A novel realization of the classical SU (2) algebra is introduced for the Dirac relativistic
hydrogen atom defining a set of operators that allow the factorization of the problem. An …

New non-unitary representations of the SU (2) algebra are introduced for the case of the
Dirac equation with a Coulomb potential; an extra phase, needed to close the algebra, is …

MATRIX ELEMENTS FOR THE ONE-DIMENSIONAL HARMONIC OSCILLATOR José L.
López-Bonilla & G. Ovando 1. Introduction One month be Page 1 MATRIX ELEMENTS FOR …

Integral relationship between Hermite and Laguerre polynomials: Its application in quantum
mechanics Page 41 The associated Laguerre polynomials can be represented by a certain …

We add a phase variable and its corresponding operator to the description of the hydrogen
atom. With the help of these additions, we device operators that act as ladder operators for …

Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the
Dirac form of relativistic quantum mechanics. Our approach is inspired by the relativistic …

In this work, we focus on some connections that exist between the Riccati and Ermakov–
Milne–Pinney equations, particularly those which are established via the Schrödinger …