Related papers: Step Momentum Operator
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 construct a discrete non-hermitean momentum operator, which implements faithfully the non self-adjoint nature of momentum for a particle in a box. Its eigenfunctions are strictly limited to the interior of the box in the continuum limit,…
For a particle in a box, the operator $- i \partial_x$ is not Hermitean. We provide an alternative construction of a momentum operator $p = p_R + i p_I$, which has a Hermitean component $p_R$ that can be extended to a self-adjoint operator,…
We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
The momentum operator for a spin-less particle when confined to a 2D surface embedded into 3D space acquires a geometrical component proportional to the mean curvature that renders it Hermitian. As a consequence, the quantum force operator…
$PT$ symmetric quantum mechanics for a particle trapped by the generalized non-Hermitian harmonic oscillator potential is studied. It is shown that energy and the expectation value of the position operator $x$ can not be real…
We develop further the concept of generalized extended momentum operator (GEMO), which has been introduced very recently in \citep{M.H2}, and propose the so called $\mathcal{PT}$-symmetric GEMO. In analogy with GEMO, the…
We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the…
Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the…
We give a modified Hamiltonian for a particle in a box with infinite potential walls that takes into account wall effects. The Hamiltonian is expressed in both the position and momentum representation. In the momentum representation 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,…
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…
A Hermitian quantum phase operator is formulated that mirrors the classical phase variable with proper time dependence and satisfies trigonometric identities. The eigenstates of the phase operator are solved in terms of Gegenbauer…
We study quantum particle dynamics in a box and driven by PT-symmetric, delta-kicking complex potential. Such dynamical characteristics as the average kinetic energy as function of time and quasi-energy at different values of the kicking…
The Hamiltonian for a spin zero particle that is confined to a curve embedded in the 3D space is constructed by squeezing the coordinates spanning a tube normal to the curve onto the curve assuming strong normal forces. We follow the new…
The real Hilbert space formalism developed within the quaternionic quantum mechanics ($\mathbb H$QM) is fully applied to the simple model of the autonomous particle. This framework permits novel insights within the usual description of the…
Based on the novel prescription for the power of a complex number, a new expression for the eigenfunction of the operator of the third component of the angular momentum is presented. These functions are normalizable, single valued and are…
We describe the dynamics of a bound state of an attractive $\delta$-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the…
A particle moving on a circle in a purely imaginary one-step potential is studied in both the exact and broken $PT$-symmetric regime.