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Particles in a Potential Well |
The treatment of n bodies with their interactions becomes impossibly complex for even small values of n. This is true for classical mechanics as well as quantum mechanics. What theorists have proposed as a workable alternative is an iterative procedure. The n bodies are assumed to create a stable field with a potential energy function. An initial trial value for the potential energy function is assumed. The motion of a particle is computed for the trial potential function without taking into account any further interaction of the particles. From the distribution of the location of the particles a modified field and potential function is then computed. This modified potential function is then used to compute a new pattern of motion and location for the particles. If this iterative procedure converges to a stable potential function and pattern of motion then the result is taken to be the solution to the problem posed.
(To be continued.)
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