Solutions of Two-dimensional Schrodinger Equation in Symmetries of Extended Quantum Mechanics for the Modified Pseudoharmonic Potential: an Application to Some Diatomic Molecules

Authors Abdelmadjid Maireche

Laboratory of Physics and Material Chemistry, Physics Department, Sciences Faculty, University of M'sila, M’sila Algeria

Issue Volume 11, Year 2019, Number 4
Dates Received 14 April 2019; revised manuscript received 08 August 2019; published online 22 August 2019
Citation Abdelmadjid Maireche, J. Nano- Electron. Phys. 11 No 4, 04013 (2019)
PACS Number(s) 11.10.Nx, 32.30 – r, 03.65 – w, 03.65.Ca, 03.65.Ge
Keywords Two dimensional Schrödinger equation, Pseudoharmonic potential, Noncommutative space-phase (3) , The Moyal-Weyl product.

The search for solutions of Schrödinger equation (SE) with physically motivated potential models has led to the discovery of new physical and chemical phenomena. For example, the pseudoharmonic oscillator potential (PHOP) has a very interesting history: it is often used to compute bound-state normalizations and energy levels of some diatomic molecules. This research has been divided into two parts. Firstly, we have converted the mechanical properties related to the force constant, the equilibrium bond length, the orthonormalized wave function and the energy eigenvalues to the corresponding atomic properties, which include the dissociation energy and equilibrium intermolecular separation for the purpose of applying to the homonuclear diatomic molecules, such as O2, N2 and H2, and heteronuclear diatomic molecules, such as CH and ScH, under 2D-PHOP. Secondly, we have investigated some aspects of the modified 2D-PHOP (2D-MPHOP) in noncommutative 2D real space-phase (NC: 2D-RSP) through the generalized Bopp’s shift method in the framework of parameters due to (space-phase) noncommutativity ( EMBED Equation.DSMT4 ) by means of the solution of the 2D-deformed SE (2D-DSE). We have reconstructed the global Hamiltonian operator for 2D-MPHOP, involving three fundamental parts: the first one is the ordinary Hamiltonian operator, in commutative quantum mechanics (CQM); the second part is the spin-orbit operator  EMBED Equation.DSMT4 , while the third one is the modified Zeeman operator  EMBED Equation.DSMT4  and corresponding energy eigenvalues by applying the perturbation method. Furthermore, we have shown that the global quantum group (GQG) of (NC: 2D-RSP) symmetries has been broken automatically and replaced by subgroup (NC: 2D-RS) under 2D-MPHOP molecules interactions. We find the energy levels of the studied homonuclear and heteronuclear diatomic molecules in CQM as special case, when we use the simultaneously two limits  EMBED Equation.DSMT4 .

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