Statistical Theory of the Error in Approximate Wavefunctions

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Abstract
The theory of how a probability distribution may be estimated by sampling is applied to the problem of using approximate wavefunctions for quantum mechanical systems and estimating the errors involved. The most probable wavefunction of given mean energy is considered and some of its properties found. The energy variance, which gives a lower bound to the true energy, can be calculated. The theory is applied to the simple harmonic oscillator and the predicted relation between mean energy and variance is compared with the actual relations found using two different types of approximate wavefunction.

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