Eigen Solution and Thermodynamic Properties of Nonrelativistic System Under the Inversely Quadratic Varshini Potential

Approximate analytical solutions of the Schrödinger equation are presented using a newly proposed Inversely Quadratic Varshini Potential (IQVP), developed as a modification of the Varshini potential. Using the Nikiforov–Uvarov functional analysis method, the energy eigenvalues and wave functions are determined. These solutions are employed to compute vibrational thermodynamic quantities. The thermodynamic trends agree well with existing literature, and numerical results are reported. The results may have potential applications in atomic, molecular, and nuclear physics.