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In this investigation a simple method developed by introducing spin to Schrödinger equation to study the relativistic hydrogen atom. By separating Schrödinger equation to radial and angular parts, we modify these parts to the associated Laguerre and Jacobi differential equations, respectively. Bound state Energy levels and wave functions of relativistic Schrödinger equation for Hydrogen atom have been obtained. Calculated results well matched to the results of Dirac's relativistic theory. Finally the factorization method and supersymmetry approaches in quantum mechanics, give us some first order raising and lowering operators, which help us to obtain all quantum states and energy levels for different values of the quantum numbers n and m.

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Energy spectrum of nucleus is one the important information for better recognition of nuclear force and interaction of nucleon inside of the nucleus. Energy levels of nucleus are measured by detecting gamma-ray energy spectrum when a target nucleus bombarded with a special projectile to excite it in to levels higher than ground state. On the other hand, there are several models to calculate nuclear energy levels. Solution of the Schrödinger equation by considering a suitable potential is direct method to obtain energy levels of a quantum mechanical system like nucleus. Projected shell model is a model of this type that is developed by solving the Schrödinger equation for a set of potentials along with role of spin. Band structure and yrast bands for even-even and odd-even isotopes of Samarium ( 159,160 Sm) are calculated using a Fortran code founded based on the projected shell model (PSM). Energy levels of negative and positive parity bands of 159 Sm and 160 Sm isotopes of Samarium nucleus are obtained separately for each spin. Kinetic and dynamic moments of inertias are also calculated for these isotopes. The acquired results are compared with the experimental data. The electromagnetic reduced transition probabilities, B(M1)/B(E2) the behavior of dynamic moment of inertia J 2 , rotational kinetic energy and moment of inertia J 1 as a function of spin have also been investigated and proper comparison is made between the calculated results and the experimental data. The alignment phenomena of neutron-proton pairs in view of the rotational movement in high spin states has also been studied with reference to band crossing.

Since 2011, he has been Head of the Department of Nuclear Physics. He has published some papers in international ISI journals of nuclear physics and presented many papers in international and national conferences. He has also published a few books. His research interests include theoretical and experimental nuclear physics, quantum mechanics and its applications, and mathematical physics. ContentsPreface XI Section Selected Topics in Foundations of Quantum Mechanics 1