Schrödinger equation with the central potentials in the discrete spectrum

P. Goded

Hadma Yuliani

The purposes of the research were to determine the energy spectrum and wave function of some q-deformed non-central shape invariance potentials, Modified Poschl-Teller plus Scarf potential and Rosen-Morse plus Rosen-Morse potential using Nikiforov-Uvarov Method. The research was a literature study to solve Schrodinger equation for qdeformed Modified Poschl-Teller plus Scarf potential and Rosen-Morse plus Rosen-Morse potential analytically. The energy spectrum and the wave functions of a system particles can be determined by Schrodinger equation. The energy spectrum and wave function for q-deformed non-central potential determined by Nikiforov-Uvarov method. Generally, the Schrodinger equation for the noncentral potential can be solved by exact if the potential variables separated into the radial and angular part. The energy spectrum and the radial wave function obtained approximately due to the centrifugal term from the radial Schrodinger equation, while the angular wave function and the orbital quantum number are obtained from angular part of Schrodinger equation. Key words: The Energy Spectrum, Wave Function, Schrodinger Equation, Non- Central, q-deformed, Nikiforov-Uvarov Method.

Victor M. Galitski, Boris Mikhailovich Karnakov, Vladimir I Kogan +1 more

Abstract This chapter analyzes problems that deal with stationary states in the discrete spectrum; the Schrödinger equation in momentum space (the Green function and integral form of the Schrödinger equation); the continuous spectrum (reflection from and transmission through potential barriers); and systems with several degrees of freedom (particle in a periodic potential).

Dedy A. Bilaut, Suparmi Suparmi, C. Cari +1 more

The 4-Dimensional Schrodinger's Equation is solved using the Supersymmetric Quantum Mechanics (SUSY QM) to obtain the first three energy spectrum and the ground state wave functions both in radial and angular parts. The non-central potential consisted of radial Scarf potential, and mix trigonometry potential such us Poschl-Teller, Rosen Morse, and Scarf for the angular part were used in this study. The energy equation of the 4-dimensional Schrodinger equation system was used to analyze some thermodynamic properties (vibrational mean energy and specific heat) of the system.

Xiaozheng Ma, Costas M. Soukoulis