Problem 1.9 – Griffith’s Intro to QM

Feb 16, 2023

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Problem 1.9

A particle of mass m has the wave function $\Psi (x,t) = Ae^{-a[(mx^2/ \hbar)+it]}$ , where $A$ and $a$ are positive real constants.

(a) Find $A$ .
(b) For what potential energy function, $V(x)$ , is this a solution to the Schrödinger equation?
(c) Calculate the expectation values of $x$ , $x^2$ , $p$ , and $p^2$ .
(d) Find $\sigma_x$ and $\sigma_p$ . Is their product consistent with the uncertainty principle?