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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Several topics related to nonlinear Schrodinger equation-(I)
非线性 薛定谔方程 量子力学
2023/11/13
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Several topics related to nonlinear Schrodinger equation-(II)
非线性 薛定谔方程 量子力学
2023/11/13
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
Derivation of the Schrodinger equation from the Hamilton-Jacobi equation in Feynman's path integral formulation of quantum mechanics
Derivation of the Schrodinger equation Hamilton-Jacobi equation Feynman's path integral formulation of quantum mechanics
2012/4/19
It is shown how the time-dependent Schr\"{o}dinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equat...
Solution of the Schrodinger equation containing a Perey-Buck nonlocality
Solution of the Schrodinger equation Perey-Buck nonlocality Computational Physics
2012/4/19
The solution of a radial Schr\"odinger equation for {\psi}(r) containing a nonlocal potential of the form \int{K(r,r') {\psi}(r') dr'} is obtained to high accuracy by means of two methods. An applicat...
On the linear forms of the Schrodinger equation
Schrodinger equation linear forms Quantum Physics
2011/10/9
Abstract: Generalizing the linearisation procedure used by Dirac and later by L\'evy-Leblond, we derive the first-order non-relativistic wave equations for particles of spin 1 and spin 3/2 starting fr...
Stationary Nonlinear Schrodinger Equation on Simplest Graphs: Boundary conditions and exact solutions
Nonlinear Schrodinger Equation Simplest Graphs Mathematical Physics
2011/9/29
Abstract: We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star graphs co...
Novel Bound States Treatment of the Two Dimensional Schrodinger Equation with Pseudocentral Plus Multiparameter Noncentral Potential
Pseudocentral potentials noncentral potential two dimensional Schrodinger equation
2011/7/28
Abstract: By converting the rectangular basis potential V(x,y) into the form as V(r)+V(r, phi) described by the pseudo central plus noncentral potential, particular solutions of the two dimensional Sc...
Convergence of the Neumann series for the Schrodinger equation and general Volterra equations in Banach spaces
Neumann Convergence the Schrodinger equation
2011/7/26
Abstract: The objective of the article is to treat the Schrodinger equation in parallel with a standard treatment of the heat equation. In the mathematics literature, the heat equation initial value p...
Dissipative periodic waves, solitons and breathers of the nonlinear Schrodinger equation with complex potentials
periodic waves solitons the nonlinear Schrodinger equation
2010/11/18
Exact solutions for the generalized nonlinear Schr\"odinger (NLS) equation with inhomogeneous complex linear and nonlinear potentials are found. We have found localized and periodic solutions for a w...
Scattering of Woods-Saxon Potential in Schrodinger Equation
Schr¨odinger equation Woods-Saxon potential Heun Function Scattering Positiondependent mass
2010/10/21
The scattering solutions of the one-dimensional Schr¨odinger equation for theWoods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and refle...
Delta function singularity in the Reduction of Radial Schrodinger Equation
Laplace operator radial equation boundary condition singular
2010/10/27
We obtain the extra delta-like singularity while reduction of the Laplace operator in
spherical coordinates, elimination of which restricts the radial wave functions at the origin. This restriction h...
Travelling wave solutions to nonlinear Schrodinger equation with self-steepening and self-frequency shift
group velocity dispersion nonlinear Schrodinger equation self-frequency shift
2010/4/7
We investigate exact travelling wave solutions of higher order nonlinear Schrodinger equation in the absence of third order dispersion. We show that this system possesses a rich solution space with a ...
Variable Separation Solution for (1+1)-Dimensional Nonlinear Models Related to Schrodinger Equation
variable separation approach (1+1)-dimensional nonlinear models
solution of soliton
2007/8/15
2004Vol.42No.4pp.568-572DOI:
Variable Separation Solution for (1+1)-Dimensional Nonlinear Models Related to Schrodinger Equation
XU Chang-Zhi1,2 and ZHANG Jie-Fang1
1 In...