Journal
PHYSICAL REVIEW E
Volume 80, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.80.022103
Keywords
Brownian motion; Green's function methods; quantum theory; Schrodinger equation
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Funding
- Israel Science Foundation
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Application of the fractional calculus to quantum processes is presented. In particular, the quantum dynamics is considered in the framework of the fractional time Schroumldinger equation (SE), which differs from the standard SE by the fractional time derivative: partial derivative/partial derivative t ->partial derivative(alpha)/partial derivative t(alpha). It is shown that for alpha=1/2 the fractional SE is isospectral to a comb model. An analytical expression for the Green's functions of the systems are obtained. The semiclassical limit is discussed.
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