G. Rawitscher, “Applications of a Numerical Spectral Expansion Method to Problems in Physics: A Retrospective,” In: T. Hempfling, Ed., Operator Theory, Advances and Applications, Vol. 203, Birkauser Verlag, Basel, 2009, pp. 409-426.

has been cited by the following article:

• TITLE: A Spectral Integral Equation Solution of the Gross-Pitaevskii Equation

  AUTHORS: George Rawitscher

  KEYWORDS: Iterative Solution of the Gross-Pitaevskii Equation; Spectral Solution of an Integral Equation;Bose-Einstein Condensates

  JOURNAL NAME: Applied Mathematics, Vol.4 No.10C, October 23, 2013

  ABSTRACT: The Gross-Pitaevskii equation (GPE), that describes the wave function of a number of coherent Bose particles contained in a trap, contains the cube of the normalized wave function, times a factor proportional to the number of coherent atoms. The square of the wave function, times the above mentioned factor, is defined as the Hartree potential. A method implemented here for the numerical solution of the GPE consists in obtaining the Hartree potential iteratively, starting with the Thomas Fermi approximation to this potential. The energy eigenvalues and the corresponding wave functions for each successive potential are obtained by a spectral method described previously. After approximately 35 iterations a stability of eight significant figures for the energy eigenvalues is obtained. This method has the advantage of being physically intuitive, and could be extended to the calculation of a shell-model potential in nuclear physics, once the Pauli exclusion principle is allowed for.