Application of the Nikiforov-Uvarov Method in Quantum Mechanics

The Nuclear Mean Field Theory and Its Application to Nuclear Physics

“…Equation (20) can be transformed into the well-known form of hypergeometric differential equation or, alternatively Nikiforo-Avorono (NU) type [13]. The obtained results using the NU method are The results obtained in this special case are in agreement with the results obtained using other methods [14].…”

Quantization of time-dependent singular potential systems in one-dimension by using the Nikiforov-Uvarov method

“…Then, we can easily identify the eigenstates of the transformed invariant operator by using a particular mathematical procedure. We use the Nikiforov-Uvarov (NU) method [20][21][22] for that purpose. This method is an alternative method for solving Schrödinger equation on the basis of a particular mathematical technique that reduces the eigenvalue equations of the invariant operator, which are second-order differential equations, to generalized hypergeometric ones [20].…”

Energy Spectra of tightly Confined Systems

“…It is based on finding a suitable coordinate transformation = ( ) to convert a general second order linear differential equation, with special orthogonal functions, into generalized hypergeometric equation of the main form (Nikiforov & Uvarov, 1988;Szego, 1975;Berkdemir, 2012) …”

“…For such cases, there are some analytical and numerical approximation methods such as 1/ expansion (Bag, Panja, & Dutt, 1992), supersymmetry (Morales, 2004), Pekeris approximation (Pekeris, 1934), variational methods (Montgomery, 2001(Montgomery, , 2011, and asymptotic iteration methods (Ciftci, Hall, & Saad, 2009) to obtain the energy eigenvalues and eigenfunctions with this type of boundary conditions. Another technique used to find exact solutions of quantum systems is the Nikiforov-Uvarov method (Nikiforov & Uvarov, 1988;Szego, 1975), which is now used often but for non confined systems by many authors.For detailed applications and applicability of the Nikiforov-Uvarov method in quantum mechanics, the reader may refer to (Berkdemir, 2012).…”