(adsbygoogle = window.adsbygoogle || []).push({}); STATEMENT:

A system is known to be in the normalized state described by the wave function

[tex]\psi(\theta,\phi)=\frac{1}{\sqrt{30}}(5Y_4^3+Y_6^3-2Y_6^0)[/tex]

What is the probaility of finding the system in a state with azmithual orbital quantum number m=3?

WHAT I HAVE:

We know that:

[tex]P=\sum_i|<Y_i^3|\psi(\theta,\phi)>|^2[/tex]

So, simply find the dot product of [tex]Y_i^3[/tex] and [tex]\psi(\theta,\phi)[/tex]. If we resolve this into the three components, this translates to:

[tex]Y_i^3 \dot \psi(\theta,\phi) = (y_1^3+y_2^3+y_3^3)\dot(5Y_4^3+Y_6^3-2Y_6^0)=(y_1^3)(5Y_4^3)+(y_2^3)(Y_6^3)-(y_3^3)(2Y_6^0)[/tex]

How can I solve this dot product without resolving the components into the solutions to the spherical harmonics? Am I missing anything, any thoughts? Thanks yall

IHateMayonnaise

EDIT: either PF changed the format for LaTeX or I turned stupid. My first LaTeX statement, within tex brackets is: \psi(\theta,\phi)=\frac{1}{\sqrt{30}}(5Y_4^3+Y_6^3-2Y_6^0). Hmmm. The following is a test of theta:

[tex]\theta[/tex]

which is (replacing []s with ()'s):

(tex)\theta(/tex)

And here is a copy/paste of the LaTeX code from another thread that IS showing up (in another thread, obviously not this one):

[tex]

\alpha\beta\chi\delta\epsilon\phi\varphi\gamma

[tex]

Which for whatever reason copies withOUT the / in the tex bracket, but still does not render. Now I've got two problems..

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# Homework Help: Probability of finding a state with azimuthal orbital quantum number

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