What Are the Most Probable Angles for a Rigid Rotor in Quantum Mechanics?

[TI-83]

Homework Statement

I am trying to find the angles (theta, phi) it is most probable to find the rigid rotor for the spherical harmonic m=1, l=1

Homework Equations

The equation given is Y = (3/8pi)^1/2*sin(theta)*e^i*phi

The Attempt at a Solution

I have tried to solve it by multiplying by the complex conjugate and setting that equal to 1. Doing so, I obtain (3/8pi)*sin²(theta) = 1 ... but from there, I can't seem to figure out how to solve for the angles (theta, phi). Any suggestions of where to go from here? Thanks!

 

[ideasrule]

I think you're misunderstanding what Y is. Y is the angular component of the wavefunction. The product of Y with its complex conjugate gives the probability density of finding the rotor at (theta,phi). Setting this product to 1 is meaningless; instead, you want to see at which angles this probability density is highest.

 

[TI-83]

I see what you're saying.

So if I set Y = (Y)(Y^*), I get that Y = (3/8pi)(sin²theta)

Therefore, I know at theta = pi/2, Y will be greatest. What is the impact of phi on this, though? Or am I just not getting it (again)?

 

[ideasrule]

phi cancels out, so the probability density does not depend on phi. This makes sense--the configuration is symmetrical about the z axis, so it wouldn't be logical for one "phi" to be favored over another.