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21. Timedependent Schrodinger equation
"... The Schrodinger equation, the basis of quantum mechanics, was discovered by Erwin Schrodinger during his skiing holiday at the end of 1925 and analyzed by him in a series of papers published in Annalen der Physik in 1926. By the end of that year, the face of physics had changed. Schrodinger won the ..."
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The Schrodinger equation, the basis of quantum mechanics, was discovered by Erwin Schrodinger during his skiing holiday at the end of 1925 and analyzed by him in a series of papers published in Annalen der Physik in 1926. By the end of that year, the face of physics had changed. Schrodinger won
Dimensional TimeDependent Schrödinger Equation
, 2016
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
ANALYSIS OF THE TOOLKIT METHOD FOR THE TIMEDEPENDANT SCHRÖDINGER EQUATION
, 907
"... Abstract. The goal of this paper is to provide an analysis of the “toolkit” method used in the numerical approximation of the timedependent Schrödinger equation. The “toolkit ” method is based on precomputation of elementary propagators and was seen to be very efficient in the optimal control frame ..."
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Abstract. The goal of this paper is to provide an analysis of the “toolkit” method used in the numerical approximation of the timedependent Schrödinger equation. The “toolkit ” method is based on precomputation of elementary propagators and was seen to be very efficient in the optimal control
On formpreserving transformations for the timedependent Schrödinger equation
, 1998
"... In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the timedependent Schrödinger equation (TDSE). In our main result, we prove that any pair of timedependent real potentials related by a Darboux transfo ..."
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Cited by 1 (0 self)
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In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the timedependent Schrödinger equation (TDSE). In our main result, we prove that any pair of timedependent real potentials related by a Darboux
On the Darboux transformation for the timedependent Schrödinger equation
, 1998
"... In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the timedependent Schrödinger equation (TDSE). The preeminent role of the latter type of transformations in the solution of the TDSE is illustrated with ..."
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In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the timedependent Schrödinger equation (TDSE). The preeminent role of the latter type of transformations in the solution of the TDSE is illustrated
An L²Estimate For The Solution To The TimeDependent Schrödinger Equation
, 1996
"... For ¸ 2 R n ; t 2 R and f 2 S (R n ) define (Sf)(t)(¸) = exp \Gamma itj¸j 2 \Delta b f(¸): We determine the optimal regularity s 0 such that Z R n k(Sf )[x]k 2 L 2 (R) dx (1 + jxj) b C kfk 2 H s (R n ) ; s ? s 0 holds where C is independent of f 2 S (R n ) or we show that such ..."
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's formula on R, orthogonality arguments arising from decomposing L 2 (R n ) using spherical harmonics and a uniform estimate for Bessel functions. Homogeneity arguments are used to show that results are sharp with respect to regularity. 0. Introduction 0.1. Let u denote the solution to the free timedependent
On Magnus Integrators for TimeDependent Schrödinger Equations
 SIAM J. Numer. Anal
, 2002
"... Numerical methods based on the Magnus expansion are an ecient class of integrators for Schrodinger equations with timedependent Hamiltonian. Though their derivation assumes an unreasonably small time step size as would be required for a standard explicit integrator, the methods perform well even f ..."
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Cited by 34 (2 self)
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Numerical methods based on the Magnus expansion are an ecient class of integrators for Schrodinger equations with timedependent Hamiltonian. Though their derivation assumes an unreasonably small time step size as would be required for a standard explicit integrator, the methods perform well even
Splitting Methods for the Timedependent Schrödinger Equation
, 1999
"... Cheap and easy to implement fourthorder methods for the Schrodinger equation with timedependent Hamiltonians are introduced. The methods require evaluations of exponentials of simple unidimensional integrals, and can be considered an averaging technique, preserving many of the qualitative prop ..."
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Cheap and easy to implement fourthorder methods for the Schrodinger equation with timedependent Hamiltonians are introduced. The methods require evaluations of exponentials of simple unidimensional integrals, and can be considered an averaging technique, preserving many of the qualitative
An RBFGalerkin Approach to the TimeDependent Schrödinger Equation
, 2012
"... In this article, we consider the discretization of the timedependent Schrödinger equation using radial basis functions (RBF). We formulate the discretized problem over an unbounded domain without imposing explicit boundary conditions. Since we can show that timestability of the discretization is ..."
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In this article, we consider the discretization of the timedependent Schrödinger equation using radial basis functions (RBF). We formulate the discretized problem over an unbounded domain without imposing explicit boundary conditions. Since we can show that timestability of the discretization
Results 1  10
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16,055