Energy levels of a physical system and eigenvalues of an operator with a singular potential

Abstract

In this paper‎, ‎we formulate the boundary value problems for second-order differential equations having singular potentials of the form $Ax^{-2}+f(x)x^{-1}+q_{0}(x)$‎, ‎where $q_{0}(x)\in L_{\mathrm{loc}}(\Omega)$ and $\Omega=(0,b)$‎. ‎First‎, ‎the existence and uniqueness theorems are proved‎, ‎and the characteristic function is constructed‎. ‎Then‎, ‎the method of providing the energy levels of singular systems is described with some examples‎