Thermodynamic properties of a charged particle in non-uniform magnetic field

We solve the Schrödinger equation for a charged particle in non-uniform magnetic field by using Nikiforov–Uvarov method. find energy spectrum and wave function, present an explicit relation partition function. give analytical expressions thermodynamic properties such as mean susceptibility, analyze entropy, free specific heat of this system numerically. It is concluded that susceptibility increase with external strength different values non-uniformity parameter, low temperature region, while mentioned quantities are decreased high regions due to increasing occupied levels at these regions. The parameter has same effect constant value on behavior properties. On other hand, results show transition from positive negative depends field.