相关论文: Quaternionic bound states
In the present study, the concept of a quantum particle with step momentum is introduced. The energy eigenvalues and eigenfunctions of such particles are obtained in the context of the generalized momentum operator, proposed recently in…
Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the…
We study the solutions to the wave equation in a two-dimensional tube of unit width comprised of two straight regions connected by a region of constant curvature. We introduce a numerical method which permits high accuracy at high…
We examine the behaviour of a charged particle in a two-dimensional confining potential, in the presence of a magnetic field. The confinement serves to remove the otherwise infinite degeneracy, but additional ingredients are required to…
The problem of a particle of mass m in the field of the inverse square potential is studied in quantum mechanics with a generalized uncertainty principle, characterized by the existence of a minimal length. Using the coordinate…
We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets…
Understanding the physical significance and spectral stability of black hole quasinormal modes is fundamental to high-precision spectroscopy with future gravitational wave detectors. Inspired by Mashhoon's idea of relating quasinormal modes…
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…
We consider here in a toy model an approach to bound state problem in a nonperturbative manner using equal time algebra for the interacting field operators. Potential is replaced by offshell bosonic quanta inside the bound state of…
Resonances in quantum mechanics are commonly introduced as quasi-bound states embedded in the continuum, a perspective that can be conceptually challenging due to the abstract nature of continuum states. In this work, we discuss an…
The effect of the uniform magnetic field on the electron in the spherically symmetric square-well potential is studied. A transcendental equation that determines the electron energy spectrum is derived. The approximate value of the lowest…
In this work, we present analytical solution of Schr\"odinger equation of confined pseudoharmonic potential in presence of a moving boundary condition, for an arbitrary angular momentum state. It turns out that an important quantity to…
An alternative approximation scheme has been used in solving the Schrodinger equation for the exponential-cosine-screened Coulomb potential. The bound state energ\i es for various eigenstates and the corresponding wave functions are…
In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an…
Relativistic equations of Bethe-Salpeter type for hadron structure are most conveniently formulated in momentum space. The presence of confining interactions causes complications because the corresponding kernels are singular. This occurs…
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We…
In this work we investigate the confining properties of charged particles of a Dirac material in the plane subject to an electrostatic potential well, that is, in an electric quantum dot. Our study focuses on the effect of mass and angular…
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…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
Entangled quantum states share properties that do not have classical analogs, in particular, they show correlations that can violate Bell inequalities. It is therefore an interesting question to see what happens to entanglement measures --…