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After a few months off (yay summer/internships), I'm 'back in the saddle' and I'm trying to catch up with my Q-mech.

I have a wave function which is given as a particle sliding freely on a circular wire:

[tex]

\Psi = A(1 + 4cos\phi)

[/tex]

I need to find the corresponding probabilities. So I know that I have to normalize the [itex]\Psi[/itex] by setting it to 1. This is split into two integrals which need to be multiplied by their complex conjugates (which are both just real values).

[tex]

\Psi = \int_{0}^{2\pi} A^2 d\phi + \int_{0}^{2\pi} A^2 16 cos^{2}\phi d\phi

[/tex]

Eventually finding, assuming my integration wasn't messed up somewhere (spoiler, I think it was)..

[tex]

\sqrt{\frac{1}{2\pi}}\Psi + \sqrt{\frac{1}{16\pi}}\Psi

[/tex]

So my probabilities are just the coefficients, right? I'm looking for a critique on this as well as I'm pretty sure I did something incorrectly.

Full question:

The wave function [itex]\Psi[/itex] where A is a normalization constant and phi is the angle the radius vector makes with the x-axis. If [itex]L_z[/itex] is measured, what are the possible outcomes and corresponding possibilities?

Thanks.

I have a wave function which is given as a particle sliding freely on a circular wire:

[tex]

\Psi = A(1 + 4cos\phi)

[/tex]

I need to find the corresponding probabilities. So I know that I have to normalize the [itex]\Psi[/itex] by setting it to 1. This is split into two integrals which need to be multiplied by their complex conjugates (which are both just real values).

[tex]

\Psi = \int_{0}^{2\pi} A^2 d\phi + \int_{0}^{2\pi} A^2 16 cos^{2}\phi d\phi

[/tex]

Eventually finding, assuming my integration wasn't messed up somewhere (spoiler, I think it was)..

[tex]

\sqrt{\frac{1}{2\pi}}\Psi + \sqrt{\frac{1}{16\pi}}\Psi

[/tex]

So my probabilities are just the coefficients, right? I'm looking for a critique on this as well as I'm pretty sure I did something incorrectly.

Full question:

The wave function [itex]\Psi[/itex] where A is a normalization constant and phi is the angle the radius vector makes with the x-axis. If [itex]L_z[/itex] is measured, what are the possible outcomes and corresponding possibilities?

Thanks.

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