Modern Physics Letters A

In this research, we consider the propagation of one-dimensional nonlinear behavior in a unmagnetized plasma. By using the reductive perturbation technique to formulate the nonlinear mathematic model which is modified Kortewege-de Vries (mKdV), we apply the extended form of two methods, which are extended auxiliary equation mapping and extended direct algebraic methods, to investigate the new families of electron-acoustic solitary wave solutions of mKdV. These new exact traveling and solitary wave solutions which represent the electrostatic potential for mKdV and also the graphical representation of electrostatic potential are shown with the aid of Mathematica.

In this work, we present a technique to obtain bounds on the generalized uncertainty principle deformation parameter by using an improved Schwarzschild solution represented by the Hayward metric in the context of scale-dependent gravity. Specifically, this deformation parameter can be interpreted in terms of a running parameter which controls the deviation from the standard Einstein–Hilbert action in the scale-dependent scenario.

We study the energy spectra of Schrödinger Hamiltonian in N-dimensional space with Coulomb plus inverse quadratic term $V(r)=-\frac{\alpha }{r}+\frac{g}{r^2}$ and energy-dependent confining potential of the form $a(E)r+b(E)r^2$. It is found that the energy spectra exhibit saturation effect, where these spectra are suppressed to finite values at large quantum numbers n and/or $\ell$ at any dimensional space N. As a typical application, we obtained a compact mass formula for the spectra of heavy quarkonia ($c\bar{c}$, $b\bar{b}$). It is found that the model is capable of reproducing the mass spectra of these systems with observed saturation governed by a factor $\gamma$. The comparison of this work predictions with available experimental data as well as other relevant theoretical works is also presented. The eigenfunctions are expressed in terms of the bi-confluent Heun functions.

It was known that a free, non-relativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current — hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has a counterpart in non-relativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.

This work aims at introducing two new solvable 1D and 3D confined potentials and present their solutions using the Tridiagonal Representation Approach (TRA). The wave function is written as a series in terms of square integrable basis functions which are expressed in terms of Jacobi polynomials. The expansion coefficients are then written in terms of new orthogonal polynomials that were introduced recently by Alhaidari, the analytical properties of which are yet to be derived. Moreover, we have computed the numerical eigenenergies for both potentials by considering specific choices of the potential parameters.

The dependence of reduced transition probabilities corresponding to electric quadrupole [B(E2)] and magnetic dipole [B(M1)] transition occurring in ${}^{18}$F nucleus on excitation energy and spin parity of the states involved in the transition has been investigated within the framework of simple potential model based on M3Y interaction. It is found that B(E2) increases with increasing excitation energy irrespective of the spin of excited states while B(M1) is very sensitive to the spin of the excited states and is independent of excitation energy.

It is shown that the stereographic coordinates on the (1 + 3)-dimensional de Sitter spacetime induce artificial singularities without physical motivation in the parametric equations of all the null or time-like geodesics on this manifold.