Fractional Schrodinger equation
Fractional Schrodinger equation
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DOI：
10.1103/physreve.66.056108
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发表时间：
2002-11-01
影响因子：
2.4
通讯作者：
Laskin, N
中科院分区：
文献类型：
--
作者：
Laskin, N
研究了分数阶薛定谔方程的一些性质。我们证明了分数阶哈密顿算符的厄米性，并建立了分数阶量子力学的宇称守恒定律。作为分数阶薛定谔方程的物理应用，我们在半经典近似下求得了类氢原子（分数阶“玻尔原子”）和分数阶振子的能谱。推导并讨论了分数阶概率流密度方程。我们还讨论了分数阶薛定谔方程和标准薛定谔方程之间的关系。
Some properties of the fractional Schrodinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schrodinger equation we find the energy spectra of a hydrogenlike atom (fractional "Bohr atom") and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schrodinger equations.