1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculate the probability that a measure on S_y yields h/2

  1. Nov 7, 2016 #1
    1. The problem statement, all variables and given/known data
    . Suppose an electron is in the spin state (a,B) If sy is measured, what is the probability of the result h/2?

    2. Relevant equations
    Eigenvectors of the pauli matrix for y are (1,i)/Sqrt[2] (1,-i)/Sqrt[2] and if you are given a wave function of the sort a | +> +b |-> then the probability of getting state | +> is a^2/(a^2+b^2)

    3. The attempt at a solution

    I wrote out (a,B) as a linear combination of the of the two eigenvectors for the pauli matrix and got that the probability of finding the electron with spin h bar/2 to be (|a-ib|^2)/2. I just want to check with all of you if that is right.
     
  2. jcsd
  3. Nov 7, 2016 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Doesn't look right to me. I assume you're just being sloppy and are using b and B to be the same variable.

    Please show the calculations you used to arrive at your answer.
     
  4. Nov 13, 2016 #3
    Certainly (a,B)=(x/Sqrt[2])(1,i)+(y/Sqrt[2])(1,-i). I solved for x and y on Mathematica and got x=(a/Sqrt[2] - iB/Sqrt[2]) and for y= a/Sqrt[2]+iB/Sqrt[2]. I then assuming a^2+B^2=1 I just took the mod square of x and got (|a-i*B|^2)/2 to be my answer. Did I do something wrong?
     
  5. Nov 13, 2016 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Nope, my mistake. Your answer is correct.

    Because you already worked out ##\lvert +_y \rangle = \frac{1}{\sqrt{2}}(\lvert + \rangle + i\lvert - \rangle)##, an easier way to arrive at the same result is to calculate the amplitude ##\lvert \langle +_y \vert (a,b) \rangle \rvert^2##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted