Hello!
"EIGENVECTOR CALCULATION IN QUANTUM MECHANICS"
This is the third part of the problem
We obtained the eigenvalues
We were working with the "Z" matrix
"v_1" is an eigenvector
"lambda_1" is an eigenvalue
We need to determine "a" and "b"
We multiply rows by columns
Both equations are equivalent
We substitute
We calculate also de bra
We obtain "v_1"
If we make the inner product we can normalize
And make the inner product equal to 1
We may write this
We have one eigenvector
It is normalized
We repeat the process for "v_2"
We need to determine two new constants
Now we apply "Z" on "v_2"
We expand
We have two equivalent equations
We can construct the next eigenvalue
We write "v_2"
We can have a common factor
We multiply both elements
We can get the normalization factor
We write the second eigenvector
Bye Bye
