Oladunjoye A. Awoga

Analytical Approximate Solution of Schrodinger Equation in D Dimensions with Quadratic Exponential-Type Potential for Arbitrary l-State

We present the bound state solution of Schrodinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov–Uvarov method to obtain the energy levels and the corresponding eigenfunction in closed form. We also compute the energy eigenvalues numerically.

Bound state solutions of d-dimensional Schrödinger equation with Eckart potential plus modified deformed Hylleraas potential

We study the d-dimensional Schrodinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov—Uvarov method. We obtain energy eigenvalues and the corresponding wave function expressed in terms of a Jacobi polynomial. We also discuss two special cases of this potential comprised of the Hulthen potential and the Rosen—Morse potential in three dimensions. Numerical results are also computed for the energy spectrum and the potentials.

On the Canonical Transformation of Time-Dependent Harmonic Oscillator

We performed a two-variable canonical transformation on the time momentum operator, and without loss of generality we carried out a three-variable transformation on the coordinate and momentum space operators to trivialize the Hamiltonian operator of the system. Fortunately, this operation separates the time-coordinate and space coordinate naturally, and the wave function of the time-dependent Harmonic Oscillator is evaluated via the generator.