In this study, the analytical solutions of the radial Schrödinger equation for the central Woods—Saxon potential together with spin-orbit interaction and centrifugal terms have been derived by using Nikiforov-Uvarov method. The energy eigenvalues and corresponding eigenfunctions of nucleons have been obtained for various values of n, l, and j quantum numbers. The obtained results using this method are in satisfactory agreement with available data in the special case.

-We discuss the relation between the quantum-mechanical survival probability of an unstable system in motion and that of the system at rest. The usual definition of the survival probability which takes into account only the time evolution of an unstable system leads to a relation between the survival probability of the system in motion and that of the system at rest which is different from the standard relation based on relativistic time dilation. This approach led other authors to claim non-standard quantum-mechanical effects which are in clear contradiction with Special Relativity. We show that an appropriate relativistic definition of the survival probability which takes into account also the space evolution of an unstable system leads to the standard relation between the survival probability of the system in motion and that of the system at rest, in agreement with Special Relativity. We present a rigorous derivation of this result based on a wave packet treatment.

We study neutrino spin oscillations in black hole backgrounds. In the case of a charged black hole, the maximum frequency of oscillations is a monotonically increasing function of the charge. For a rotating black hole, the maximum frequency decreases with increasing the angular momentum. In both cases, the frequency of spin oscillations decreases as the distance from the black hole grows. As a phenomenological application of our results, we study simple bipolar neutrino system which is an interesting example of collective neutrino oscillations. We show that the precession frequency of the flavor pendulum as a function of the neutrino number density will be higher for a charged/non-rotating black hole compared with a neutral/rotating black hole respectively.

By using WKB method and considering deformed Woods–Saxon nuclear potential, deformed Coulomb potential, and centrifugal potential, the alpha decay half-lives of 68 superheavy alpha emitters have been calculated. The effect of the constant value of surface diffuseness parameter in the range of 0.1 [Formula: see text]a [Formula: see text] 0.9 (fm) on the potential barrier, tunneling probability, assault frequency, and alpha decay half-lives has been investigated. Significant differences were observed for alpha decay half-lives and decay quantities in this range of surface diffuseness. Good agreement between calculated half-lives with fitted surface diffuseness parameter a = 0.54 (fm) and experiment was observed.

We study the spectrum of hydrogen atom, Lamb shift and Stark effect in the framework of simultaneous space–space and momentum–momentum (s-s, p-p) noncommutative quantum mechanics. The results show that the widths of Lamb shift due to noncommutativity is bigger than the one presented in Ref. 1. We also study the algebras of observables of systems of identical particles in s-s, p-p noncommutative quantum mechanics. We introduce θ-deformed su(2) algebra.