Extension of perturbation theory to quantum systems with conformable derivative

In this paper, the perturbation theory is extended to be applicable for systems containing conformable derivative of fractional order [Formula: see text]. This is needed as an essential and powerful approximation method for describing systems with conformable differential equations that are difficult to solve analytically. The work here is derived and discussed for the conformable Hamiltonian systems that appears in the conformable quantum mechanics. The required [Formula: see text]-corrections for the energy eigenvalues and eigenfunctions are derived. To demonstrate this extension, three illustrative examples are given, and the standard values obtained by the traditional theory are recovered when [Formula: see text].

Intensity-dependent nonlinear optical properties in an asymmetric Gaussian potential quantum well modulated by external fields

In this paper, the effects of external electric, magnetic and non-resonant intense laser fields on the nonlinear optical rectification (NOR), second-harmonic (SH), and third-harmonic (TH) generation in a GaAs quantum well with asymmetrical Gaussian potential are theoretically investigated. Firstly, the energy eigenvalues and eigenfunctions of a single electron confined in the structure are obtained by using the diagonalization method within the framework of the effective-mass and parabolic band approaches. Then, using these energy eigenvalues and eigenfunctions, expressions derived within the compact density matrix approximation has been employed to calculate the coefficients of the nonlinear optical response in the structure. The obtained simulation results show that the influence of the external fields leads to significant changes in the coefficients of nonlinear optical rectification, second and third harmonic generation in the system. As a result, it has been seen that the amplitude and position of the peaks of nonlinear optical rectification, second and third harmonic coefficients can be controlled by changing the applied external fields.

Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

<p class="Abstract">The energy eigenvalues and eigenfunctions of Dirac equation for Rosen Morse plus Rosen Morse potential are investigated numerically in terms of finite Romanovsky Polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials. The energi eigen value is solved by numerical method with Matlab 2011.</p>

Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

<p class="Abstract">The energy eigenvalues and eigenfunctions of Dirac equation for Rosen Morse plus Rosen Morse potential are investigated numerically in terms of finite Romanovsky Polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials. The energi eigen value is solved by numerical method with Matlab 2011.</p>

Exactly separable Bohr Hamiltonian with the Morse potential for triaxial nuclei

In this paper, the Morse potential is used in the β-part of the collective Bohr Hamiltonian for triaxial nuclei. Energy eigenvalues and eigenfunctions are obtained in a closed form through exactly separating the Hamiltonian into its variables by using an appropriate form of the potential. The results are applied to generate the nuclear spectrum of 192 Pt , 194 Pt and 196 Pt isotopes which are known to be the best candidate exhibiting triaxiality. Electric quadrupole transition ratios are calculated and then compared with the experimental data and the Z(5) model results.

GALILEAN COVARIANT DIRAC EQUATION WITH A WOODS–SAXON POTENTIAL

We derive and solve the Galilean covariant Dirac equation, also called "Lévy-Leblond equation", for spin-½ particles in a Woods–Saxon potential. We obtain this wave equation with a Galilean covariant approach, which is based on a (4+1)-dimensional manifold with light-cone coordinates followed by a reduction to the (3+1)-dimensional Galilean space-time. We apply the Pekeris approximation and exploit the Nikiforov–Uvarov method to find the energy eigenvalues and eigenfunctions.

ABSENCE OF DIQUARKS IN S-WAVE BARYONS

We analyze the dynamics of diquark formation in baryons containing one light and two heavy quarks. Due to the slower motion of the heavy quarks, we consider the motion of the light quark in a reference frame fixed in the two heavy ones. The potential of the light quark interacting with the two heavy quarks is derived from the quark–antiquark potential in mesons. This potential has a repulsive barrier between the two heavy quarks. A variational approach similar to that used in the study of the hydrogen molecule is applied to determine the two lowest energy eigenvalues and eigenfunctions of the light quark. The time-dependent wave function obtained describes the oscillation of the light quark along the direction defined by the two heavy quarks. We observe that the energy of this oscillating state is higher than the repulsive barrier between the two heavy quarks. There is no tunneling in the oscillation of the light quark, so we conclude that there is not formation of clusters or metastable states of a heavy and a light quark in this kind of baryons.