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The eigenvalue equations for the energy of bound states of a particle in a square well are solved, and the exact solutions are obtained, as power series. Accurate analytical approximate solutions are also given. The application of these…
We present solutions to a set of problems that arise in quantum entanglement theory, whose common trait is the use of algebraic methods. The backbone of the thesis consists of two general theorems, pertaining to specific convex sets of…
In this paper, we implement a quantum algorithm -on IBM quantum devices, IBM QASM simulator and PPRC computer cluster -to find the energy values of the ground state and the first excited state of a particle in a finite square-well…
The effects of quantum fluctuations in fields confined by background configurations may be simply and transparently computed using the Green's function approach pioneered by Schwinger. Not only can total energies and surface forces be…
Quantum computing is a new computational paradigm with the potential to solve certain computationally challenging problems much faster than traditional approaches. Civil engineering encompasses many computationally challenging problems,…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
We obtain an analytic solution for a three-parameter class of logarithmic potentials at zero energy. The potential terms are products of the inverse square and the inverse log to powers 2, 1 and 0. The configuration space is the…
In this work we present a semi-classical approach to solve the inverse spectrum problem for one-dimensional wave equations for a specific class of potentials that admits quasi-stationary states. We show how inverse methods for potential…
We consider a semilinear wave equation in the whole space with a deep potential well. We prove that as the depth of the well tends to infinity, the solutions of the equation converge to the solutions of a wave equation defined on the bottom…
A new family of 2-component vector-valued coherent states for the quantum particle motion in an infinite square well potential is presented. They allow a consistent quantization of the classical phase space and observables for a particle in…
We analyze here the energy states and associated wave functions available to a particle acted upon by a delta function potential of arbitrary strength and sign and fixed anywhere within a one-dimensional infinite well. We consider how the…
We present a class of confining potentials which allow one to reduce the one-dimensional Schroodinger equation to a named equation of mathematical physics, namely either Bessel's or Whittaker's differential equation. In all cases, we…
In this paper, we study the Schr\"odinger equation with Dunkl derivative for a free particle confined in a cylindrical potential well. We consider both the finite and infinite height cases. The Dunkl formalism introduces reflection…
The main goal of this work is to solve the nonrelativistic wave equation for a new potential configuration that describes the quantum states of a particle that lies within a onedimensional infinite well of width L using the Asymptotic…
We construct the regularised Wheeler-De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for a subset of all wavefunctions being integrals of scalar densities this condition can be…
We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated…
The procedure commonly used in textbooks for determining the eigenvalues and eigenstates for a particle in an attractive Coulomb potential is not symmetric in the way the boundary conditions at $r=0$ and $r \rightarrow \infty$ are…
The numerical solution of partial differential equations by discretization techniques is ubiquitous in computational physics. In this work we benchmark this approach in the quantum realm by solving the heat equation for a square plate…
New exact results are given for the interior Casimir energies of infinitely long waveguides of triangular cross section (equilateral, hemiequilateral, and isosceles right triangles). Results for cylinders of rectangular cross section are…
Developing high-performance materials is critical for diverse energy applications to increase efficiency, improve sustainability and reduce costs. Classical computational methods have enabled important breakthroughs in energy materials…