Determination of the eigenfunctions of arbitrary nanostructures using time domain simulation

  • Sullivan D
  • Citrin D
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With the present interest in nanostructures, such as quantum dots, there is a need to have a flexible method with which to be able to determine eigenvalues and eigenstates for those structures that do not lend themselves to existing analytical methods. In this article we present a method that accomplishes this by using a simulation of the Schrödinger equation based on the finite-difference time-domain method. This method is capable of simulating any structure within the limits of discretization. By initializing a simulation with a test function, the eigenfrequencies are determined through a Fourier transform of the resulting time-domain data collected at a sample point. Another simulation implements a discrete Fourier transform at the eigenfrequencies at every cell in the problem space, from which the eigenfunctions can be constructed.

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  • Dennis M. Sullivan

  • D. S. Citrin

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