Related papers: Schrodinger equation for classical particles
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…
Schroedinger's equation with scalar and vector potentials is shown to describe "nothing but" hopping of a quantum particle on a lattice; any spatial variation of the hopping amplitudes acts like an external electric and/or magnetic field.…
Electromagnetic particle is considered as appropriate particle solution of nonlinear electrodynamics. Mass, spin, charge, and dipole moment for the electromagnetic particle are defined. Classical motion equations for massive charged…
Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also…
Recent studies have shown that the use of Dunkl derivatives instead of ordinary derivatives leads to deriving parity-dependent dynamic solutions. According to this motivation in this manuscript, we formulate the Dunkl-Schr\"odinger equation…
An approximate method is proposed to solve position dependent mass Schr\"odinger equation. The procedure suggested here leads to the solution of the PDM Schr\"odinger equation without transforming the potential function to the mass space or…
A general form of the effective mass Schrodinger equation is solved exactly for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the…
We obtain exact solutions of the 2D Schr\"odinger equation for Hydrogen atom with the lenear and Harmonic Potentials in noncommutative complex space, using the Power-series expansion method. Hence we can say that the Schr\"odinger equation…
In this note we propose a new set of coordinates to study the hyperbolic or non-elliptic cubic nonlinear Schrodinger equation in two dimensions. Based on these coordinates, we study the existence of bounded and continuous hyperbolically…
We report the exact fundamental solution for Kramers equation associated to a brownian gas of charged particles, under the influence of homogeneous (spatially uniform) otherwise arbitrary, external mechanical, electrical and magnetic…
We look for positive solutions to the nonlinear Schrodinger equation with a potential, under the hypothesis of zero mass on the nonlinearity, in a particular situation. Existence and multiplicity results are provided.
An unsolved problem of classical mechanics and classical electrodynamics is the search of the exact relativistic equations of motion for a classical charged point-particle subject to the force produced by the action of its EM self-field.…
If $\Psi$ is a quaternionic wave function, then $i\Psi\neq \Psi i$. Thus, there are two versions of the quaternionic Schr\"odinger equation (QSE). In this article, we present the second possibility for solving the QSE, following on from a…
We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for $\vert x\vert >a$ and an arbitrary function for $\vert x\vert <a$, using elementary methods. The study of this…
Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical…
The local phase-invariance of the momentum-space Schr\"odinger equation for free-particle has been used to construct quantum kinematics that describes a motion of the particle in external U(1) background gauge field. The gauge structure…
The black hole model with a self-gravitating charged spherical symmetric dust thin shell as a source is considered. The Schroedinger-type equation for such a model is derived. This equation appeared to be a finite differences equation. A…
We prove asymptotic completeness in the energy space for the nonlinear Schrodinger equation posed on hyperbolic space in the radial case, in space dimension at least 4, and for any energy-subcritical, defocusing, power nonlinearity. The…
We study the particle creation process in the Schwinger model coupled with an external classical source. One can approach the problem by taking advantage that the full quantized model is solvable and equivalent to a (massive) gauge field…
Most authors of textbooks on quantum mechanics either postulate or sketch a short `ad hoc` derivation of Schrodinger's equation. In this work we give a detailed derivation of Schrodinger's equation from the Hamilton-Jacobi equation and the…