The time-dependent Schrodinger equation is a square-preserving and symplectic(SPS)transformation.The canonical'equations of quantum systems are deduced by using eigenfanction expansion.The normal-square of wavefun...The time-dependent Schrodinger equation is a square-preserving and symplectic(SPS)transformation.The canonical'equations of quantum systems are deduced by using eigenfanction expansion.The normal-square of wavefunction of the quantum systems is an invariant integral of the canonical equations and then the symplectic schemes that based on both Cayley transformation and diagonal Fade approximation to exp(x)are also sq uare-preserving.The evaluated example show that the SPS approach is reasonable and effective for solving time-evolution of quantum system.展开更多
基金Supported by the National Natural Science Foundation of ChinaState Commission of Science and Technologythe State Education Commission。
文摘The time-dependent Schrodinger equation is a square-preserving and symplectic(SPS)transformation.The canonical'equations of quantum systems are deduced by using eigenfanction expansion.The normal-square of wavefunction of the quantum systems is an invariant integral of the canonical equations and then the symplectic schemes that based on both Cayley transformation and diagonal Fade approximation to exp(x)are also sq uare-preserving.The evaluated example show that the SPS approach is reasonable and effective for solving time-evolution of quantum system.
