(adsbygoogle = window.adsbygoogle || []).push({}); <p> and <p^2> for uniform "psi"

1. The problem statement, all variables and given/known data

What is <p> and <p^2> for state:

[tex]\begin{array}{l}

\psi (x) = {\rm{constant for x}} \in {\rm{[ - a,a]}} \\

\psi (x) = {\rm{0 for x}} \notin {\rm{[ - a,a]}} \\

\end{array}[/tex]

....that is: a "psi" that is constant within a finite region [-a, +a], and zero everywhere else. (No calculus required!).

2. Relevant equations

[itex]\left\langle {{p_x}} \right\rangle = \left\langle {\psi \left| { - {\bf{i}}{\textstyle{\partial \over {\partial x}}}} \right|\psi } \right\rangle [/itex]

3. The attempt at a solution

[itex]\left\langle p \right\rangle ,\left\langle {{p^2}} \right\rangle = 0[/itex]

...right? I think so, because d/dx(constant) = 0. For a wavefunction that doesn't change, you have a particle that ain't moving, right? I think this is a simple question, but I'm having a dropped-brain moment...

Oh yes: if <p> and <p^2> = 0, then: momentum is exactly known to be 0, so why isn't position-uncertainty infinite?

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# Homework Help: <p> and <p^2> for uniform psi

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