Finding the probability of an electron

[apott155]

Homework Statement

Determine the probability of finding the electron in the region for which the psi 320 wavefunction is negative(toroidal region).

Homework Equations

The Attempt at a Solution

cos (theta)=+/- sqrt 1/3

radial part integrated= r^6*e^(-2r/3a)

Angular part= (9cos(theta)^4-6cos(theta)^2+1)sin(theta)

 

[fzero]

Can you use the roots cos (theta)=+/- sqrt 1/3 to determine a range of \theta for which the angular part of the wavefunction is negative?

 

[apott155]

YUp.

 

[apott155]

I tried that, but I don't see where the radial part comes in

 

[fzero]

Can the radial part of the wavefunction ever be negative? Note that the quantities you wrote down are the squares of the relevant factors of the wavefunction. (they're also not normalized).

 

[apott155]

I don't think so... The ending value has to be inbetween 0 and 1 because its probability

 

[fzero]

I don't think so... The ending value has to be inbetween 0 and 1 because its probability

Be careful. |\Psi|^2 is positive and bounded, but \Psi itself isn't so restricted. In this case you need to examine the functional form.