(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

My wavefunction is [tex]\psi (r, \theta, \phi )=N cos(\theta) e^{-(r/R_0)^2}[/tex].

I need to calculate [tex]<p_r>[/tex] and [tex]\Delta p_r[/tex] where [tex]p_r[/tex] is the radial momentum.

2. Relevant equations

I think i know [tex]p_r=\frac{\hbar}{i} \left( \frac{d}{dr}+\frac{1}{r} \right) [/tex].

3. The attempt at a solution

When I try to calculate the observation value I got infinity (the integral does not seem to converge):

[tex]<\psi | p_r | \psi > = \int_0^{2 \pi}d\phi \int_0^\pi d\theta \int_0^{\infty}dr [\psi^\star p_r \psi] [/tex]

Are the limits for the integral correct? What am I doing wrong? :(

thank.

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# Homework Help: Quantum mechanics: free partical in spherical coordinates

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