Problem 1.3 – Griffith’s Intro to QM

Feb 16, 2023

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Problem 1.3

Consider the gaussian distribution

$\rho (x) = Ae^{-\lambda (x-a)^2}$

where $A$ , $a$ , and $\lambda$ are positive real constants. (The necessary integrals are inside the back cover.)
(a) Use Equation 1.16 to determine $A$ .
(b) Find $\langle x \rangle$ , $\langle x^2 \rangle$ , and $\sigma$ .
(c) Sketch the graph of $\rho (x)$ .