RIEMANNIAN QUANTUM ENERGY OF A PARTICLE IN A FINITE-POTENTIAL WELL

In this research work, the golden Riemannian Laplacian operator was constructed using the golden metric tensor in spherical polar coordinate and was applied to the Schrodinger wave equation in order to obtain the golden Riemannian Schrodinger equation for a particle in a finite-potential well. The golden Riemannian Schrodinger equation was solved analytically to obtain the particle energy. The solution resulted to two expressions for the energy of a particle in a finite-potential well. One of the expressions is for the odd energy levels while the other is for the even energy levels. The results are that the golden Riemannian Laplacian operator and golden Riemannian Schrodinger equations were augmented with additional terms which are not found in the existing equations; and this can be applied to a finite-potential well problem so as to obtain the corresponding expression for the energy values.