We show how, using the constructive approach for special functions introduced by Nikiforov and Uvarov, one can obtain recurrence relations for the hypergeometric-type functions not only for the continuous case but also for the discrete and q-linear cases, respectively. Some applications in Quantum Physics are discussed. 2000 Mathematics Subject Classification: 33C45, 33D45

Exact bound state solutions of the Schrödinger equation for generalized noncentral potential are examined by means of the Nikiforov-Uvarov method. The wavefunctions and the corresponding energy eigenvalues of the system are obtained analytically. The results examined for the potential are compatible with those obtained by the other methods.

We present the exact supersymmetric solution of Schrödinger equation with the Morse, Pöschl-Teller and Hulthén potentials by using the Nikiforov-Uvarov method. Eigenfunctions and corresponding energy eigenvalues are calculated for the first six excited states. Results are in good agreement with the ones obtained before. PACS numbers: 03.65.Ge, 12.39.Jh

The Klein-Gordon equation in D-dimensions for a recently proposed Kratzer potential plus ring-shaped potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound-states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the noncentral equal scalar and vector potentials. The results obtained in this work are m...

Using supersymmetric approach, the Schrödinger equation for various potentials can be exactly solved. In this work, the solutions of Schrödinger equation for Eckart potential is exactly obtained via the Nikiforov-Uvarov method. The corresponding energy eigenstates and energy eigenvalue of Hamiltonian analytically are found. PACS: 12.20.-m; 11.80.-m; 11.80.Et

In this work we develop a simple theoretical framework for asynchronous point-to-point communication which can be seen as a generalization of the detection and isolation model introduced in (Nikiforov, 1995). A notion of capacity is defined and corresponding upper and lower bounds are derived.

We investigate complex PT and non-PT-symmetric forms of the generalized WoodsSaxon potential. We also look for exact solutions of the Schrödinger equation for the PT and/or non-PT-symmetric potentials of the kind mentioned above. Nikiforov-Uvarov method is used to obtain their energy eigenvalues and associated eigenfunctions. PACS:03.65.Fd, 03.65.Ge, 02.30.Gp

Combinatorics, Probability & Computing / Volume 11 / Issue 02 / March 2002, pp 179 189 DOI: 10.1017/S0963548301004928, Published online: 25 April 2002 Link to this article: http://journals.cambridge.org/abstract_S0963548301004928 How to cite this article: V. NIKIFOROV (2002). Some Inequalities for the Largest Eigenvalue of a Graph. Combinatorics, Probability & Computing, 11, pp 179-189 doi:10.1...

In this paper we will prove that μ(G) + μ(G) ≤ 1 + √ 3 2 n − 1 where μ(G), μ(G) are the greatest eigenvalues of the adjacency matrices of the graph G and its complement and n denotes the number of vertices of G.