Abstract
In some quantum chemical applications, the potential models are linear combination of single exactly solvable potentials. This is the case equivalent of the Stark effect for a charged harmonic oscillator (HO) in a uniform electric field of specific strength (HO in an external dipole field). We obtain the exact s-wave solutions of the Dirac equation for some potential models which are linear combination of single exactly solvable potentials (ESPs). In the framework of the spin and pseudospin symmetric concept, we calculate analytical expressions for the energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by using the Nikiforov-Uvarov (NU) method, in closed form. The nonrelativistic limit of the solution is also studied and compared with the other works.
Highlights
The Schrödinger equation provides an insight to the fundamental quantum chemical problems
This solution can be done by using the supersymmetry (SUSY) [3,4], the NikiforovUvarov (NU) method [5], the asymptotic iteration method (AIM) [6], the exact quantization rule (EQR) [7] and the tridiagonal J-matrix method (TJM) [8], etc
The electron confinement in harmonic oscillator (HO) potential exposed to n external electric field is one of the quantum chemical applications
Summary
The Schrödinger equation provides an insight to the fundamental quantum chemical problems. There are a number of solvable nonrelativistic quantum problems in which all the energy eigenvalues and wave functions are explicitly known from different operator methods [1] and analytical procedures [2] specially developed to solve the desired wave equation. The electron confinement in harmonic oscillator (HO) potential exposed to n external electric field is one of the quantum chemical applications This is well known as charged HO in a uniform electric field or an HO in an external dipole field. The SUSY and shape invariance methods have been used to determine ESPs are extended to obtain the energy eigenvalues and their generalized partner potentials [11] It demands the existence of the Witten superpotential W ( x) [12] associated with the ESPs in order to find the witten superpotential for the combined potential.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
