The Time Fractional Schrodinger Equation on Hilbert Space

被引：21

作者：

Gorka, Przemyslaw ^{[1
]}

Prado, Humberto ^{[2
]}

Trujillo, Juan ^{[3
]}

机构：

[1] Warsaw Univ Technol, Dept Math & Informat Sci, Ul Koszykowa 75, PL-00662 Warsaw, Poland

[2] Univ Santiago Chile, Dept Matemat & Ciencia Comp, Casilla 307 Correo 2, Santiago, Chile

[3] Univ La Laguna, Dept Anal Matemat, Tenerife, Spain

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2017年 / 87卷 / 01期

关键词：

Fractional quantum mechanics; Caputo derivative; Schrodinger equation;

D O I：

10.1007/s00020-017-2341-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the linear fractional Schrodinger equation on a Hilbert space, with a fractional time derivative of order and a self-adjoint generator A. Using the spectral theorem we prove existence and uniqueness of strong solutions, and we show that the solutions are governed by an operator solution family . Moreover, we prove that the solution family converges strongly to the family of unitary operators e(-itA), as approaches to 1.

引用

页码：1 / 14

页数：14

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