integrals - For example suppose we want to calculate 2 2 ax...

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Chem. 540 Notes on Integrals Functions of the form 2 ( ) , Re 0 ax bx f x e a - + = are called Gaussian. Integrals of Gaussian functions occur frequently in quantum mechanics. It can be shown that 2 2 / 4 ax bx b a e dx e a π - + -∞ = . One not so well known techniques for evaluating certain integrals is to take a derivative with respect to a parameter.
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Unformatted text preview: For example, suppose we want to calculate 2 2 ax x e dx ∞--∞ ∫ . Notice that 2 2 , ax x e a-∂ = -∂ so we find 3 2 2 2 2 1 2 ax ax x e dx e dx a a a a ∞ ∞----∞-∞ ∂ ∂ = -= -= ∂ ∂ ∫ ∫ . ERROR: undefined OFFENDING COMMAND: STACK:...
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