相关论文: Justification for the group-theoretical method as …

We compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum…

We use group theoretic methods to obtain the extended Lie point symmetries of the quantum dynamics of a scalar particle probing the near horizon structure of a black hole. Symmetries of the classical equations of motion for a charged…

We examine the classical problem of an infinite square well by considering Hamilton's equations in one dimension and Hamilton-Jacobi equation for motion in two dimensions. We illustrate, by means of suitable examples, the nature of the…

We solve the infinite potential well problem using the methods of Heisenberg's matrix mechanics. In addition to being of educational value, the matrix mechanics allows us to deal with various unphysical issues caused by this potential in a…

We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping $w \to z = w…

An infinite square well with a discontinuous step is one of the simplest systems to exhibit non-Newtonian ray-splitting periodic orbits in the semiclassical limit. This system is analyzed using both time-independent perturbation theory (PT)…

The group-theoretic approach is used to construct exact solutions to perfect fluid equations invariant under the Schrodinger group, or the l-conformal Galilei group, or the Lifshitz group. In each respective case, the velocity vector field…

We use group theoretic methods to obtain the extended Lie point symmetries of the equations of motion for a charged particle in the field of a monopole. Cases with certain model magnetic fields and potentials are also studied. Our analysis…

There are various types of infinite potential well problems occurring in elementary quantum mechanics formalism. The infinite square well (one dimensional), cubical box and, spherical well are quite common in textbooks. In this paper, we…

The theory of higher derivative gravity is proposed to solve the non-renormalizable problem in quantum gravity.In this article, We use two numerical methods to fit another static spherically symmetric black hole besides the Schwarzschild…

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,…

A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.

This paper present how to solve the problem of cylindrical quantum wells with potential energy different from zero and with singularity of the energy on the axis of the cylinder. The solution to the problem was obtained using methods of…

Within the framework of fractional quantum mechanics, an exact solution has been found for the energy spectrum of a quantum particle confined in a quantum well - a symmetric one-dimensional finite potential well. A simple graphical…

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…

Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…

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…

We extend the standard treatment of the asymmetric infinite square well to include solutions that have zero curvature over part of the well. This type of solution, both within the specific context of the asymmetric infinite square well and…

Efficiently simulating quantum circuits on classical computers is a fundamental challenge in quantum computing. This paper presents a novel theoretical approach that achieves substantial speedups over existing simulators for a wide class of…

Different features of a potential in the form of a Gaussian well have been discussed extensively. Although the details of the calculation are involved, the general approach uses a variational method and WKB approximation, techniques which…