Abstract
Integrals of products ofn-dimensional, displaced, simple harmonic-oscillator (SHO) wave functions are evaluated. Each of thep different wave functions may be displaced in both representation and momentum space. Each SHO wave function may be an eigensolution of a different integral or differential equation. These integrals occur in quantum mechanics, coherent optics and nonlinear optics. In addition, the notation and formalism introduced in this work may prove useful in other areas of mathematical physics. We provide a more powerful and versatile alternative to the Einstein summation convention. The coherent-state representation of Glauber is adapted to the discussion of the above integrals.
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