Continuous-time random walk as a guide to fractional Schroedinger equation

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3491333· OSTI ID:21476481

Lenzi, E K; Ribeiro, H V; Mukai, H; Mendes, R S ^[1]

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1. Departamento di Fisica, Universidade Estadual de Maringa, Avenida Colombo 5790, Maringa, Parana 87020-900 (Brazil)

We argue that the continuous-time random walk approach may be a useful guide to extend the Schroedinger equation in order to incorporate nonlocal effects, avoiding the inconsistencies raised by Jeng et al. [J. Math. Phys. 51, 062102 (2010)]. As an application, we work out a free particle in a half space, obtaining the time dependent solution by considering an arbitrary initial condition.

• OSTI ID: 21476481
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 9; Other Information: DOI: 10.1063/1.3491333; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFUSION
GRAPH THEORY
MARKOV PROCESS
MATHEMATICAL SOLUTIONS
QUANTUM MECHANICS
RANDOMNESS
SCHROEDINGER EQUATION
SPACE
TIME DEPENDENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
STOCHASTIC PROCESSES
WAVE EQUATIONS