- #1

Syrus

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## Homework Statement

This problem comes from the second edition of Griffiths's,

*Introduction to Quantum Mechanics*.

Given the Gaussian Distribution: p(x) = Ae

^{c(x-a)2}

find <x>, that is, the expectation (or mean) value of x.

Clearly, to do this you evaluate the following integral: ∫xp(x)dx on (-∞,∞). I've tried performing this integration analytically, and it seems to be more bothersome than a rectal exam. The solution should be x = a since, by definition, p is centered at x = a (this is evident graphically as well). Is a qualitative solution sufficient here? Another method (which obviously does not work in general) is to set p'(x) = 0 and solve for x since we know the Gaussian distrubtion contains only one extremum. Any advice on the best means to proceed?