Thermal and Quantum Properties of Nonlinear and Inverted Harmonic Oscillators in Magnetic Fields: Applications to Polyatomic Molecules

Abstract

An analytical study of the radial Schrodinger wave equation with magnetic field, nonlinear and inverted nonlinear isotropic harmonic oscillator potentials was carried out. A modified substitution technique was used to determine the energy eigenvalues of the nonlinear and inverted nonlinear oscillators while the Laplace and computational methods were used to determine the radial wave functions. The determination of the energies’ eigenvalues and the radial wave functions enabled the study to generate tables, plot graphs, and discuss the effect of the magnetic field, angular frequency, and nonlinear term on the thermodynamic functions and systems. Results of the study revealed that the energies’ eigenvalues of the inverted nonlinear oscillator fluctuates increasingly and decreasingly, while that of the nonlinear isotropic oscillator fluctuates decreasingly and degeneracies, completely removed. As the angular frequency is improved, expansion or increase is observed in the nonlinear and the inverse nonlinear cases in the radial wave functions. In the case of increase in the nonlinear term, saturation in the radial wave functions are observed in the inverted and non-inverted cases. For the effect of the increase in the magnetic field potential, initial decrease with saturation was observed in the both cases. The effect of the magnetic field and nonlinear term in both the nonlinear and inverted oscillators on the thermodynamic functions, attained saturation on the polyatomic molecules, while the effects of angular frequency is observed to enhance the thermodynamic functions. Generally, the contraction or saturation experienced with the increase of the magnetic field term is as a result of the small value of the electron charge, and the carbon (iv) oxide molecule is at higher potential than that of the water molecule.