ﻻ يوجد ملخص باللغة العربية
A covariant non-local extention if the stationary Schrodinger equation is presented and its solution in terms of Heisenbergss matrix quantum mechanics is proposed. For the special case of the Riesz fractional derivative, the calculation of corresponding matrix elements for the non-local kinetic energy term is performed fully analytically in the harmonic oscillator basis and leads to a new interpretation of non local operators in terms of generalized Glauber states. As a first application, for the fractional harmonic oscillator the potential energy matrix elements are calculated and the and the corresponding Schrodinger equation is diagonalized. For the special case of invariance of the non-local wave equation under Fourier-transforms a new symmetry is deduced, which may be interpreted as an extension of the standard parity-symmetry.
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described by the wa
In this paper, we establish the existence of ground state solutions for a fractional Schrodinger equation in the presence of a harmonic trapping potential. We also address the orbital stability of standing waves. Additionally, we provide interesting
Lie point symmetries of the 2+1-dimensional cubic Schrodinger equation to obtain new analytic solutions in a systematic manner. We present an analysis of the reduced ODEs, and in particular show that although the original equation is not integrable t
New exact analytical bound-state solutions of the radial Dirac equation in 3+1 dimensions for two sets of couplings and radial potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generali
In this paper we investigate the one-dimensional harmonic oscillator with a singular perturbation concentrated in one point. We describe all possible selfadjoint realizations and we show that for certain conditions on the perturbation exactly one neg