带有时间－空间分数阶导数的广义Schrodinger方程
Generalized fractional schrodinger equation
本文中，作者首先建立了带有时间和空间分数阶导数的广义Schrodinger方程。借助于积分变换的方法，例如Fourier变换和Laplace变换，求解了自由粒子在方势阱中的解，并用Mittag-Leffler函数来表示。另外，本文还讨论了广义Schrodinger方程的几个例子和经典的量子力学的关系。
In this paper the generalized fractional Schrodinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function. Finally, we discuss the relationship between the cases of the generalized fractional Schrodinger equation and the ones in standard quantum.
王少伟、徐明瑜
物理学
chrodinger方程，分数阶导数，积分变换，量子力学
Schrodinger equation fractional calculus integral transform quantum mechanics
王少伟,徐明瑜.带有时间－空间分数阶导数的广义Schrodinger方程[EB/OL].(2006-10-30)[2025-08-16].http://www.paper.edu.cn/releasepaper/content/200610-550.点此复制
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