It is shown that the Schr\"odinger nonrelativistic equation of a system of interacting particles is not a rigorously nonrelativistic equation since it is based on the implicit assumption of finiteness of the interaction propagation velocity. For a system of interacting particles, a fully nonrelativistic nonlinear system of integro-differential equations is proposed. In the case where the size of the system of particles is of the same order as the Compton wavelength associated with particles, certain essential differences are shown to exist as compared with traditional consequences of the nonrelativistic Schr\"odinger equation.It is shown that the Schr\"odinger nonrelativistic equation of a system of interacting particles is not a rigorously nonrelativistic equation since it is based on the implicit assumption of finiteness of the interaction propagation velocity. For a system of interacting particles, a fully nonrelativistic nonlinear system of integro-differential equations is proposed. In the case where the size of the system of particles is of the same order as the Compton wavelength associated with particles, certain essential differences are shown to exist as compared with traditional consequences of the nonrelativistic Schr\"odinger equation.

arXiv:quant-ph/0002012Physical Review ADec 8, 19993 citations

Nonrelativistic one-particle problem on $q$ -deformed Euclidean spaceNonrelativistic one-particle problem on $q$-deformed Euclidean space

Hartmut Wachter

We consider time-dependent Schrödinger equations for a free nonrelativistic particle on the three-dimensional $q$ -deformed Euclidean space. We determine plane wave solutions to these Schrödinger equations and show that they form a complete orthonormal system. We derive $q$ -deformed expressions for propagators of a nonrelativistic particle. Considerations about expectation values for position or momentum of a nonrelativistic particle conclude our studies.We consider time-dependent Schrödinger equations for a free nonrelativistic particle on the three-dimensional $q$-deformed Euclidean space. We determine plane wave solutions to these Schrödinger equations and show that they form a complete orthonormal system. We derive $q$-deformed expressions for propagators of a nonrelativistic particle. Considerations about expectation values for position or momentum of a nonrelativistic particle conclude our studies.

arXiv:2010.08826Oct 17, 20200 citations

Nonrelativistic one-particle problem on

q

-deformed Euclidean space

We consider time-dependent Schrödinger equations for a free nonrelativistic particle on the three-dimensional

q

-deformed Euclidean space. We determine plane wave solutions to these Schrödinger equations and show that they form a complete orthonormal system. We derive

q

-deformed expressions for propagators of a nonrelativistic particle. Considerations about expectation values for position or momentum of a nonrelativistic particle conclude our studies.