How Do You Calculate Electron Spin Probabilities from a Wavefunction?

[land]

Simple question regarding spin :)

Homework Statement

An electron is in spin state (superposition of spin eigenstates) given by the wavefunction: $$\chi=\frac{1}{3}\chi_+ + \frac{2\sqrt{2}}{3}\chi_-$$. I need to find the probabilities that a measurement would find the electron with spin up or spin down.

Homework Equations

Uh.. you just square the coefficients, right? :)

The Attempt at a Solution

Probably a silly question but this seems too easy. I don't have this as a formula anywhere in my notes or book.. but to find the probability of spin up, you just square (1/3), and to find the probability of spin down, it's just the square of 2sqrt(2)/3... right?

 

[OlderDan]

Homework Statement

An electron is in spin state (superposition of spin eigenstates) given by the wavefunction: $$\chi=\frac{1}{3}\chi_+ + \frac{2\sqrt{2}}{3}\chi_-$$. I need to find the probabilities that a measurement would find the electron with spin up or spin down.

Homework Equations

Uh.. you just square the coefficients, right? :)

The Attempt at a Solution

Probably a silly question but this seems too easy. I don't have this as a formula anywhere in my notes or book.. but to find the probability of spin up, you just square (1/3), and to find the probability of spin down, it's just the square of 2sqrt(2)/3... right?

If it's properly normalized, that will do it.

 

[land]

If it's properly normalized, that will do it.

Thanks! :)