相关论文: A quantum mechanical well and a derivation of a $\…
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 consider the quantum mechanical behavior of a driven particle in an infinite 1D potential well. We show that the time dependent perturbation series is induced by the delicate non-trivial properties of the momentum operator in this case,…
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…
Using a recent reformulation of quantum mechanics where the potential function is not required, we are able to obtain the energy spectrum and wave function associated with the infinite square well analytically. Therefore, this work…
Energy spectrum of an electron confined by finite hard-wall potential in a cylinder quantum dot placed in weak (up to 100 kOe) homogeneous external magnetic field were calculated using the method of variation of vector potential. Electronic…
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 ${8 m}{w^2} / h^2$,…
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…
We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle $2\theta_0$ emanating from the center of the sphere, with $0<\theta_0<\pi$. This non-central…
A Gedanken experiment is described to explore a counter-intuitive property of quantum mechanics. A particle is placed in a one-dimensional infinite well. The barrier on one side of the well is suddenly removed and the chamber dramatically…
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…
In the present paper a method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. Starting with the problem of a reflection from an impenetrable wall, the obtained solution is then…
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…
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…
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…
A famous pre-Newtonian formula for $\pi$ is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions.
The momentum entropic moments and R\'enyi entropies of a one-dimensional particle in an infinite well potential are found by means of explicit calculations of some Dirichlet-like trigonometric integrals. The associated spreading lengths and…
In this short paper, we propose a new quantum effect that naturally emerges from describing the quantum particle as a classical fluid. Following the hydrodynamical formulation of quantum mechanics for a particle in a finite convex region,…
Recently, a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian $H=p^2+x^2(ix)^\epsilon$ was studied. It was found that the energy levels for this theory are real for all $\epsilon\geq0$. Here, the…
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,…
Context: Due to advances in synthesizing lower dimensional materials there is the challenge of finding the wave equation that effectively describes quantum particles moving on 1D and 2D domains. Jensen and Koppe and Da Costa independently…