- #1
Rahmuss
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[SOLVED] Eigenvalues and Eigenspinors
(a) Find the eigenvalues and eigenspinors of [tex]S_{y}[/tex].
[tex]\hat{Q}f(x) = \lambda f(x)[/tex]
The above equation wasn't given specifically for this problem; but that's the one I'm trying to use.
[tex]\hat{Q}f(x) = \lambda f(x)[/tex] --> [tex]\frac{\hbar}{2}\left(^0_i ^-i_0\right) f(x) = \lambda f(x)[/tex]
But here is where I'm stuck. I'm not sure what I would be using for my function [tex]f(x)[/tex]. I guess the fact that it's a matrix kind of throws me off too.
For the second part (finding the eigenspinors of [tex]S_{y}[/tex]), so far I have:
[tex]X_{+}y = \frac{\hbar}{2}\left(^{0}_{i} ^{-i}_{0}\right)[/tex] --> [tex]\frac{\hbar}{2}\left(^{0}_{i}\right)[/tex]
P.S. I'm not quite sure how to do matrices in this tex code. Does anyone know how?
Homework Statement
(a) Find the eigenvalues and eigenspinors of [tex]S_{y}[/tex].
Homework Equations
[tex]\hat{Q}f(x) = \lambda f(x)[/tex]
The Attempt at a Solution
The above equation wasn't given specifically for this problem; but that's the one I'm trying to use.
[tex]\hat{Q}f(x) = \lambda f(x)[/tex] --> [tex]\frac{\hbar}{2}\left(^0_i ^-i_0\right) f(x) = \lambda f(x)[/tex]
But here is where I'm stuck. I'm not sure what I would be using for my function [tex]f(x)[/tex]. I guess the fact that it's a matrix kind of throws me off too.
For the second part (finding the eigenspinors of [tex]S_{y}[/tex]), so far I have:
[tex]X_{+}y = \frac{\hbar}{2}\left(^{0}_{i} ^{-i}_{0}\right)[/tex] --> [tex]\frac{\hbar}{2}\left(^{0}_{i}\right)[/tex]
P.S. I'm not quite sure how to do matrices in this tex code. Does anyone know how?