Ita O. Akpan

Bound State Solutions of the Schrödinger Equation for a More General Woods—Saxon Potential with Arbitrary l-State

The energy spectra and the wave function depending on the c-factor are investigated for a more general Woods—Saxon potential (MGWSP) with an arbitrary l-state. The wave functions are expressed in terms of the Jacobi polynomials. Two potentials are obtained from this MGWSP as the special cases. These special potentials are Hulthen and the standard Woods—Saxon potentials. We also discuss the energy spectrum and wave function for the special cases.

Exact Solutions of Schrodinger Equation with Improved Ring-Shaped Non-Spherical Harmonic Oscillator and Coulomb Potential

We propose improved ring shaped like potential of the form, V(r, θ) = V(r) + (ħ2/2Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2 and its exact solutions are presented via the Nikiforov–Uvarov method. The angle dependent part V(θ) = (ħ2 / 2 Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2, which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.

Bound-State Solutions of the Klein-Gordon Equation with -Deformed Equal Scalar and Vector Eckart Potential Using a Newly Improved Approximation Scheme

We present the analytical solutions of the Klein-Gordon equation for q-deformed equal vector and scalar Eckart potential for arbitrary -state. We obtain the energy spectrum and the corresponding unnormalized wave function expressed in terms of the Jacobi polynomial. We also discussed the special cases of the potential.

Quantum Damped Mechanical Oscillator

The exact solutions of the Schrodinger equation for quantum damped oscillator with modified Caldirola-Kanai Hamiltonian are evaluated. We also investigate the cases of under-, over-, and critical damping.

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.