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

"The angular part of the wave function for the dxy orbital is (√(15/∏)/4)sin^2(θ)sin(2[itex]\phi[/itex]). Show that this expression corresponds to the dxy orbital"

2. Relevant equations

conversion of Cartesian to spherical coordinates:

r=√(x^2+y^2+z^2)

cosθ=z/r

tan([itex]\phi[/itex])=y/x

trig identity:

sin(2x)=2sinxcosx

normalization:

N^2∫ψ*ψdτ

dτ=r^2sinθdrdθd[itex]\phi[/itex]

0≤r≤∞

0≤θ≤∏

0≤[itex]\phi[/itex]≤2∏

3. The attempt at a solution

in Cartesian coordinates dxy is represented as simply xy. I converted xy to spherical coordinates and manipulated the equation the relevant equations to get xy=(r/2)sin^2(θ)sin(2[itex]\phi[/itex]) as follows:

xy=rsincos[itex]\phi[/itex]rsinθsin[itex]\phi[/itex]

xy=rsin^2(θ)cos[itex]\phi[/itex]sin[itex]\phi[/itex]

xy=rsin^2(θ)sin(2[itex]\phi[/itex])/2

Then I tried to normalize the equation, but I ended up with

∫r^3 from 0 to ∞, which goes to ∞/does not converge

and ∫sin2[itex]\phi[/itex] which equal zero.

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# Homework Help: Prove the wave function for dxy orbital

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