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A quantum anharmonic oscillator is defined by the Hamiltonian ${\cal H}= -\frac{ {\rm d^{2}}}{{\rm d}x^{2}} + V(x)$, where the potential is given by $V(x) = \sum_{i=1}^{m} c_{i} x^{2i}$ with $c_{m}>0$. Using the Sinc collocation method…
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
We extend the approach of [Smith et al. 2019] to derive analytical expressions for the eigenvalues and eigenmatrices of an isotropic membrane energy density function $\psi : \mathbb{R}^{3x2} \to \mathbb{R}$. Clamping the eigenvalue…
In this work, the beta-decay halflives problem is dealt as a nonlinear optimization problem, which is resolved in the statistical framework of Machine Learning (LM). Continuing past similar approaches, we have constructed sophisticated…
The behavior of polyatomic molecules around their equilibrium positions can be regarded as quantum coupled anharmonic oscillators. Solving the corresponding Schr\"odinger equations can interpret or predict experimental spectra of molecules.…
Using the one-dimensional potential well with realistic parameters for atomic nuclei, we illustrate the movement of the poles of the S-matrix, and the transmission coefficient when the well supports an anti-bound state. We calculate the…
The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are…
In recent years, artificial neural network (ANN) has been successfully applied in nuclear physics and some other areas of physics. This study begins with the calculations of {\alpha}-decay half-lives for some neutron-deficient nuclei using…
Effects of various nuclear interaction potentials on the decay lifetimes and the turning points of the WKB action integral has been studied. The microscopic nuclear potential obtained by folding in the density distribution functions of the…
A model consisting of a Harmonic Oscillator well and a linear potential, coupled by Dirac delta function, is solved. We find the exact analytical expressions for Green's function for this problem. This Green's functions are used to…
The eigenvalues and eigenfunctions of a linear {\alpha}^{2}-dynamo have been computed for different spatial distributions of an isotropic \alpha-effect. Oscillatory solutions are obtained when \alpha exhibits a sign change in the radial…
Stability of 248-254^Cf nuclei against alpha and cluster emission is studied within our Coulomb and proximity potential model (CPPM). It is found that these nuclei are stable against light clusters (except alpha particle) and instable…
Nuclear physics seeks to describe both bound and unbound states within a unified predictive framework. While coordinate-space Quantum Monte Carlo (QMC) methods have successfully computed bound states for systems with $A \leq 12$, their…
The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are…
Microscopic investigations for the observed properties of the recently reported five unstable new isotopes are carried out. The ground state properties are calculated in the relativistic mean field (RMF) framework and the results reproduce…
The decimal logarithm of spontaneous fission half-life of the superheavy nucleus $^{286}$Fl experimentally determined is $\log_{10} T_f^{exp} (s) = -0.632$. We present a method to calculate the half-life based on the cranking inertia and…
Basing on the relation between the Coulomb Green function and the Green function of harmonic oscillator, the algebraic representation of the many-particle Coulomb Green function in the form of annihilation and creation operators is…
Assuming linearity of the perturbations at the time of decoupling, we reconstruct the primordial scalar potential from the temperature and polarization anisotropies in the cosmic microwave background radiation. In doing so we derive an…
Theoretical decay half-lives of the heaviest odd-Z nuclei are calculated using the experimental Q value. The barriers in the quasimolecular shape path are determined within a Generalized Liquid Drop Model (GLDM) and the WKB approximation is…
A quantum mechanical model for the description of the alpha-decay of heavy nuclei with accompanying photons emission is presented. The model is based on a quantum mechanical one-particle model of alpha-decay through a decay barrier. The…