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## Homework Statement

This is Exercise 9 from chapter 15 of merzbacer. It asks to find [itex]\lvert\psi(x,t)\rvert^2[/itex] given:

[tex]

\psi(x,t)=[2\pi(\Delta x)_0^2]^{-1/4}\left[1+\frac{i\hbar t}{2m(\Delta x)_0^2} \right]^{-1/2} \exp\left[\frac{-\frac{x^2}{4(\Delta x)_0^2}+ik_0x-ik_0^2\frac{\hbar t}{2m}}{1+\frac{i\hbar t}{2m(\Delta x)_0^2}}\right]

[/tex]

## Homework Equations

[tex]\lvert\psi(x,t)\rvert^2=\psi^*(x,t)\psi(x,t)[/tex]

[tex](\Delta x)^2=\langle x \rangle^2 - \langle x^2\rangle[/tex]

[tex]i\hbar\frac{d}{dt}\langle A \rangle = \langle[A,H]\rangle + \left\langle\frac{\partial A}{\partial t} \right\rangle[/tex]

## The Attempt at a Solution

My question is quick and qualitative: is there..an easier way of doing this than the brute force way? I mean, am I not seeing something? Or is this problem as useless as it seems?

I am not allowed to use a computer in any way.

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