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knowlewj01
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Homework Statement
an operator for a system is given by
[itex]\hat{H}_0 = \frac{\hbar \omega}{2}\left[\left|1\right\rangle\left\langle1\right| - \left|0\right\rangle\left\langle0\right|\right][/itex]
find the eigenvalues and eigenstates
Homework Equations
The Attempt at a Solution
so i formulated this operator as a matrix
[itex]\frac{\hbar \omega}{2}
\left( \begin{array}{cc}
-1 & 0 \\
0 & 1 \\ \end{array} \right)
[/itex]
and found the eigenvalues to be -1 and 1
but when i put them back into the eigenvalue equation Hx = λx [x is a 2 row column vector with elements x1 and x2]
i get nonsense, something like
for λ=1:
x1 = -x1
x2 = x2
for λ=-1:
x1 = x1
x2 = -x2
am i missing something important here?
thanks.