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Simulation of Time-Dependent Schrödinger Equation in the Position and Momentum Domains

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DOI: 10.4236/ajcm.2015.53027    3,590 Downloads   4,128 Views  

ABSTRACT

The paper outlines the development of a new, spectral method of simulating the Schrödinger equation in the momentum domain. The kinetic energy operator is approximated in the momentum domain by exploiting the derivative property of the Fourier transform. These results are compared to a position-domain simulation generated by a fourth-order, centered-space, finite-difference formula. The time derivative is approximated by a four-step predictor-corrector in both domains. Free-particle and square-well simulations of the time-dependent Schrödinger equation are run in both domains to demonstrate agreement between the new, spectral methods and established, finite-difference methods. The spectral methods are shown to be accurate and precise.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Jennings, M. (2015) Simulation of Time-Dependent Schrödinger Equation in the Position and Momentum Domains. American Journal of Computational Mathematics, 5, 291-303. doi: 10.4236/ajcm.2015.53027.

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