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Chinese Control Conference (CCC)

Solution of Schrödinger Equation Based on State Transition Matrix

Xing Yifan, Xiao Qinwen, Diyang Chu, Xice Sun, Jun Yong Wu

Published Jul 1, 2006• 1 citation
Publisher

Abstract

Based on the systematic discussion of normalization and the matrix representation of operator, we use state transition matrix to derive the solutions for stationary and non-stationary Schrodinger equation. Unlike the matrix representation of eigenstate in quantum information, this paper presents a matrix solution theory for superposition state, and provides a theoretical basis for applying the means of control to quantum systems.

DOI
10.1109/chicc.2006.4347594

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Based on the systematic discussion of normalization and the matrix representation of operator, we use state transition matrix to derive the solutions for stationary and non-stationary Schrodinger equation. Unlike the matrix representation of eigenstate in quantum information, this paper presents a matrix solution theory for superposition state, and provides a theoretical basis for applying the means of control to quantum systems.
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A method is proposed for the quantum-mechanical determination of the eigenstates and eigenvalues of a particle (e.g. an electron) in a potential of general shape. For such systems the method allows one to calculate the exact solutions of the stationary Schrödinger equation. For the application of this method any well-known reference system is needed. A transition from the stationary reference system to the stationary system under investigation is performed by means of the time-dependent Schrödinger equation. The results are compared with various standard methods; alternative numerical methods will be discussed critically.