Related papers: Symbolic Solution for Generalized Quantum Cylindri…
Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum…
Quantum computation strongly relies on the realisation, manipulation and control of qubits. A central method for realizing qubits is by creating a double-well potential system with a significant gap between the first two eigenvalues and the…
Exact solutions, in terms of special functions, of all wave equations $% u_{xx} - u_{tt} = V(x) u(t,x)$, characterised by eight inequivalent time independent potentials and by variable separation, have been found. The real valueness of the…
Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schr\"odinger equation to obtain molecular energies has been demonstrated to scale polynomially with system…
A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the…
We compute the ground state energy of a massive scalar field in the background of a cylindrical shell whose potential is given by a delta function. The zero point energy is expressed in terms of the Jost function of the related scattering…
Firstly we derive peculiar spherical Weyl solutions, using a general spherically symmetric metric due to a massive charged object with definite mass and radius. Afterwards, we present new analytical solutions for relevant cosmological…
In this paper, we consider Einstein-Hilbert gravity in the presence of cosmological constant with cylindrical symmetry to introduce the black hole solution of this model. Here, we solve the Einstein's vacuum field equation, and then we…
A simple decay model is introduced. The model comprises of a point potential well, which experiences an abrupt change. Due to the temporal variation the initial quantum state can either escape from the well or stay localized as a new bound…
This article presents a mathematical framework for solving Maxwell's equations in cylindrical and spherical geometries with continuous angular indices. We extend beyond standard discrete harmonic decomposition to a continuous spectral…
An integral equation-based numerical method for scattering from multi-dielectric cylinders is presented. Electromagnetic fields are represented via layer potentials in terms of surface densities with physical interpretations. The existence…
We calculate the exact Casimir interaction energy between two perfectly conducting, very long, eccentric cylindrical shells using a mode summation technique. Several limiting cases of the exact formula for the Casimir energy corresponding…
Using mainly two techniques, a point transformation and a time dependent supersymmetry, we construct in sequence several quantum infinite potential wells with a moving barrier. We depart from the well known system of a one-dimensional…
An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency $\omega$ and the difference of the minima is close to a multiple of $\hbar \omega$. A WKB wave function is constructed…
We present an efficient and robust semi-analytical formulation to compute the electric potential due to arbitrary-located point electrodes in three-dimensional cylindrically stratified media, where the radial thickness and the medium…
We explore the quantum nature of black holes by introducing an effective framework that takes into account deviations from the classical results. The approach is based on introducing quantum corrections to the classical Schwarzschild…
We use the discrete approach to solve the Schr\"odinger as well as the Bloch equations for a free particle and the quantum gas of free particles embedded in an infinite quantum well with the finite width. We obtain the expressions of energy…
This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The…
Quantum Wells (QW) are of great importance in optoelectronic devices such as LEDs and LASERs, being the emissive layers.Simulating the quantum particles in different QW topologies like rectangular finite potential wells, multiple potential…
Using supersymmetric quantum mechanics we construct the quasi-exactly solvable (QES) potentials with arbitrary two known eigenstates. The QES potential and the wave functions of the two energy levels are expressed by some generating…