Related papers: Symbolic Solution for Generalized Quantum Cylindri…
We demonstrate that certain class of infinite sums can be calculated analytically starting from a specific quantum mechanical problem and using principles of quantum mechanics. For simplicity we illustrate the method by exploring the…
We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the…
The local Casimir energy density and the global Casimir energy for a massless scalar field associated with a $\lambda\delta$-function potential in a 3+1 dimensional circular cylindrical geometry are considered. The global energy is examined…
We review recent work on the Casimir interaction energy between cylindrical shells. We include proposals for future experiments involving cylinders, such us a null experiment using quasi-concentric cylinders, a cylinder in front a…
The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three…
The finite square potential well is a staple problem in introductory quantum mechanics. There is an extensive literature on the determination of the allowed energies, which requires the solution of a transcendental equation by numerical,…
We give a lower bound for the energy of a quantum particle in the infinite square well. We show that the bound is exact and identify the well-known element that fulfils the equality. Our approach is not directly dependent on the…
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts…
We describe an example of an exact, quantitative Jeopardy-type quantum mechanics problem. This problem type is based on the conditions in one-dimensional quantum systems that allow an energy eigenstate for the infinite square well to have…
We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…
Besides the standard quantum version of the Coulomb/Kepler problem, an alternative quantum model with not too dissimilar phenomenological (i.e., spectral and scattering) as well as mathematical (i.e., exact-solvability) properties may be…
One dimensional quantum mechanics problems, namely the infinite potential well, the harmonic oscillator, the free particle, the Dirac delta potential, the finite well and the finite barrier are generalized for finite arbitrary dimension in…
A chart for the quantum mechanics of a particle of mass $m$ in a one-dimensional potential well of width $w$ and depth $V_0$ is derived. The chart is obtained by normalizing energy and potential through multiplication by ${8 m}{w^2} / h^2$,…
This paper deals with the partial solution of the energy eigenvalue problem for generalized symmetric quartic oscillators. Algebraization of the problem is achieved by expressing the Schroedinger operator in terms of the generators of a…
Recently, the problem of the infinite spherical well was solved by the group-theoretical method to resolve all the peculiarities in the currently accepted solution [DOI: 10.13140/RG.2.2.18172.44162 (Researchgate, 2017)]. With a view to…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
We suggest a mathematical potential well with spherical symmetry and apply to the 1d Schr\"odinger equation. We use some well-known techniques as Stationary Perturbation Theory and WKB to gain insight into the solutions and compare them to…
We study axisymmetric solution to the conformally invariant wave equation on a Kerr background by means of numerical and analytical methods. Our main focus is on the behaviour of the solutions near spacelike infinity, which is appropriately…
The vacuum (Casimir) energy in quantum field theory is a problem relevant both to new nanotechnology devices and to dark energy in cosmology. The crucial question is the dependence of the energy on the system geometry under study. Despite…
The Casimir energy of a semi-circular cylindrical shell is calculated by making use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symmetry axes of…