Related papers: Square-well potential in quaternic quantum mechani…
It is shown that the quaternionic Hilbert space formulation of quantum mechanics allows a quantization, based on a generalized system of imprimitivity, that leads to a description of the motion of a quantum particle in the field of a…
Quantum mechanics provides several methods to generate and securely distribute private lists of numbers suitably correlated to solve the Three Byzantine Generals Problem. So far, these methods are based on three-qutrit singlet states,…
We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. We solve the Schr\"odinger equation in terms of Weber functions and discuss the behavior of the eigenvalues and eigenfunctions. We derive the…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
From a careful study of the transcendental equations fulfilled by the bound state energies of a free particle in a quantum well, cylindrical wire or spherical dot with finite potential barrier, we have derived analytical expressions of…
We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there no known polynomial algorithm (classical or quantum)…
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory…
Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. In this article the first- and second- order supersymmetric transformations will be used to obtain new…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
The quantum engine cycle serves as an analogous representation of the macroscopic nature of heat engines and the quantum regime of thermal devices composed of a single element. In this work, we follow the formalism of a quantum engine…
We consider the following first order systems of mathematical physics. 1.The Dirac equation with scalar potential. 2.The Dirac equation with electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The system describing…
We revisit the Schr\"{o}dinger equation of a quantum particle that is confined on a curved surface. Inspired by the novel work of R. C. T. da Costa [1] we find the field equation in a more convenient notation. The contribution of the…
Using the notion of quantum integers associated with a complex number $q\neq 0$, we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little $q$-Jacobi polynomials when $|q|<1$, and…
We address two questions regarding square-well potentials from a didactic perspective. The first question concerns whether or not the justification of the standard a priori omission of the potential's vertical segments in the analysis of…
For an understanding of a heat engine working in the microscopic scale, it is often necessary to estimate the amount of reversible work extracted by isothermal expansion of the quantum gas used as its working substance. We consider an…
Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between…
One of the most important issues of quantum engineering is the construction of low-dimensional structures possessing desirable properties. For example, in different areas of possible applications of the structures containing quantum wells…
In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones…
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…
We discuss solutions of the spherically symmetric wave equation and Klein Gordon equation in an arbitrary number of spatial and temporal dimensions. Starting from a given solution, we present various procedures to generate futher solutions…