Exact solutions of the time-dependent Schrödinger equation for pseudoharmonic potentials

Lu-Ya Wang, Xiaoyan Gu, Zhong-Qi Ma +1 more

Victor F. Los, Nicholas V. Los

K. J. Oyewumi, F. O. Akinpelu, Adetomiwa Agboola

Alexander S. Chikhachev

Tapas Das, Altuğ Arda

The second-order N -dimensional Schrödinger equation with pseudoharmonic potential is reduced to a first-order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution theorem. Some special cases are verified and variations of energy eigenvalues En as a function of dimension N are furnished. To give an extra depth of this paper, the present approach is also briefly investigated for generalized Morse potential as an example.

A. N. Ikot, I. B. Okon, U. S. Okorie +8 more

Abstract In this work, we find the exact solution of Schrödinger wave equation for position dependent mass with pseudoharmonic oscillator using extended Nikiforov-Uvarov method. We obtained the energy-eigen equation presented in a closed and compact form and used the result to study both superstatistics and thermodynamic properties by first determining the partition function of the system. The unnormalized wave function was obtained and expressed in terms of Confluent Heun function. Using the resulting energy eigen equation, the numerical computation were computed for varying masses for with fixed physical constant potential parameter λ. The numerical result shows that the bound state energies increase with quantum states but decreases with the dependent mass m(x). The thermodynamics and superstatistics plots are also reported.