effective potential from the generalized time-dependent schrödinger equation

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ID: 207689
2016
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Abstract
We analyze the generalized time-dependent Schrödinger equation for the force free case, as a generalization, for example, of the standard time-dependent Schrödinger equation, time fractional Schrödinger equation, distributed order time fractional Schrödinger equation, and tempered in time Schrödinger equation. We relate it to the corresponding standard Schrödinger equation with effective potential. The general form of the effective potential that leads to a standard time-dependent Schrodinger equation with the same solution as the generalized one is derived explicitly. Further, effective potentials for several special cases, such as Dirac delta, power-law, Mittag-Leffler and truncated power-law memory kernels, are expressed in terms of the Mittag-Leffler functions. Such complex potentials have been used in the transport simulations in quantum dots, and in simulation of resonant tunneling diode.
Reference Key
sandev2016mathematicseffective Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Trifce Sandev;Irina Petreska;Ervin K. Lenzi
Journal Turkish journal of pharmaceutical sciences
Year 2016
DOI
10.3390/math4040059
URL
http://www.mdpi.com/2227-7390/4/4/59
Keywords
effective potential

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