相关论文: Geometric description of the Schr\"odinger equatio…

In this paper the one-dimensional nonparaxial nonlinear Schr\"odinger equation is considered. This was proposed as an alternative to the classical nonlinear Schr\"odinger equation in those situations where the assumption of paraxiality may…

From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…

The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian…

We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…

With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin,…

We use the "tridiagonal representation approach" to solve the time-independent Schr\"odinger equation for the bound states of generalized versions of the trigonometric and hyperbolic P\"oschl-Teller potentials. These new solvable potentials…

In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schr\"odinger equations to higher-order Schr\"odinger equations with a more general nonlinearity. More precisely, we consider a…

In scaled relational particle mechanics, only relative times, relative angles and relative separations are meaningful. It arose in the study of the absolute versus relative motion debate. It has then turned out to be a useful toy model of…

Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…

Dynamics of a free point particle on a multi world-line is presented and shown to reduce to that of a bosonic string theory at the appropriate limit. Other higher dimensional extended objects are argued to appear at other regions of the…

This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…

We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…

The equations governing null and timelike geodesics are derived within the 3+1 formalism of general relativity. In addition to the particle's position, they encompass an evolution equation for the particle's energy leading to a 3+1…

We consider a two-component system of cubic nonlinear Schr\"odinger equations in one space dimension. We show that each component of the solutions to this system behaves like a free solution in the large time, but there is a strong…

A duality between an electrostatic problem in a three dimensional world and a quantum mechanical problem in a one dimensional world which allows one to obtain the ground state solution of the Schr\"odinger equation by using electrostatic…

In this survey the contemporary results concerning supersymmetries in generalized Schr\"odinger equations are presented. Namely, position dependent mass Sch\"odinger equations are discussed as well as the equations with matrix potentials.…

In this short paper I discuss how conformal geometric algebra models for euclidean and minkowski targetspaces determine the allowed quantum mechanical statespaces for free particles. I explicitly treat 2-dimensional euclidean space and…

We prove that the effective low-energy, nonlinear Schroedinger equation for a particle in the presence of a quasiperiodic potential is the potential-free, nonlinear Schroedinger equation on noncommutative space. Thus quasiperiodicity of the…

We start by formulating geometrically the Newton's law for a classical free particle in terms of Riemannian geometry, as pattern for subsequent developments. In fact, we use this scheme for further generalisation devoted to a constrained…

We embed Nelson's stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative theory of quantum mechanics on (pseudo)-Riemannian manifolds. Within this approach, we derive stochastic…