Local pinning of trial wave functions: An optimization method without integrals for finding approximate solutions of field equations
Date
2010Author
Theodorakis, StavrosKindyni, N.
Source
American Journal of PhysicsVolume
78Issue
3Pages
244-249Google Scholar check
Metadata
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We present an optimization method that requires no integrations for obtaining approximate solutions of field equations of the form F(Ψ(r{combining right arrow above}))=0. The expression F(Ψ(r{combining right arrow above})) would be identically zero everywhere if Ψ(r{combining right arrow above}) were an exact solution. The method consists of selecting an appropriate trial function Ψ0(r{combining right arrow above}), which depends on several parameters, and requiring that the values of these parameters be such that F(Ψ0(r{combining right arrow above})) equal zero in certain regions of space, especially around singularities. This requirement yields a locally pinned trial wave function that approximates the exact solution. We illustrate the method by applying it to a simple harmonic oscillator, a vortex in a superfluid, to the ground state of a Bose-Einstein condensate and to the ground state of the helium atom. © 2010 American Association of Physics Teachers.