Related papers: Application of Hellman-Feynman and Hypervirial the…
Having in mind applications to gravitational wave theory (in connection with the radiation reaction problem), stochastic semiclassical gravity (in connection with the regularization of the noise kernel) and quantum field theory in…
An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The…
In solid-state physics, energies of crystals are usually computed with a plane-wave discretization of Kohn-Sham equations. However the presence of Coulomb singularities requires the use of large plane-wave cut-offs to produce accurate…
In this work we solve the Schr\"odinger equation for Bohr Hamiltonian with Coulomb and Hulth\'en potentials within the formalism of minimal length in order to obtain analytical expressions for the energy eigenvalues and eigenfunctions by…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator and the screened Coulomb potential is developed. Based upon the $\hbar$-expansions and suitable…
Eigenvalues of the Breit Equation {eqnarray*} [(\vec{\alpha}_{1} \vec{p} + \beta_{1}m)_{\alpha \alpha^{\prime}} \delta_{\beta \beta^{\prime}} + \delta_{\alpha \alpha^{\prime}} (-\vec{\alpha}_{2} \vec{p} + \beta_{2}M)_{\beta \beta^{\prime}}…
We provide a link between the virial theorem in functional analysis and the method of multipliers in theory of partial differential equations. After giving a physical insight into the techniques, we show how to use them to deduce the…
In this article I study different possibilities of analytically solving the Sturm-Liouville problem with variable coefficients of sufficiently arbitrary behavior with help of perturbation theory. I show how the problem can be reformulated…
In this study, we give the variation of parameters method from a different viewpoint for the Nth order inhomogeneous linear ordinary difference equations with constant coefficient by means of delta exponential function . Advantage of this…
The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing…
For the $S$ states of two-electron atoms, we introduce an exact and unique factorization of the internal eigenfunction in terms of a marginal amplitude, which depends functionally on the electron-nucleus distances $r_1$ and $r_2$, and a…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive…
In the present article a family of quantum anharmonic oscillators is studied using Hermite's function basis (Fock's basis) in the Hilbert space. The numerical investigation of the eigenenergies of that family is presented. The statistical…
We review the well-known Hellmann Feynman Theorem (HFT), originally developed for Hermitian systems to facilitate the calculation of forces among the molecules. Our work extends this foundational theorem to the domain of non-Hermitian…
In this work, we investigate the quantum motions of non-relativistic particles interacting with a potential in the presence of the Aharonov-Bohm (AB) flux field within a topological defect geometry, for example, space-time with a distortion…
How does the inclusion of the gravitational potential alter an otherwise exact quantum mechanical result? This question motivates this report, with the answer determined from an edited version of problem #12 on p.273 of Ref.1. To elaborate,…
We calculate the exceptional points of the eigenvalues of several parameter-dependent Hamiltonian operators of mathematical and physical interest. We show that the calculation is greatly facilitated by the application of the discriminant to…
Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with…
A recently proposed algorithm to obtain global solutions of the double confluent Heun equation is applied to solve the quantum mechanical problem of finding the energies and wave functions of a particle bound in a potential sum of a…
While perturbation theories constitute a significant foundation of modern quantum system analysis, extending them from the Hermitian to the non-Hermitian regime remains a non-trivial task. In this work, we generalize the…