- #1
ultimateguy
- 125
- 1
Homework Statement
A is a non-Hermitian operator. Show that
[tex]i(A-A^t)[/tex]
is a Hermitian operator.
Homework Equations
[tex]\int \psi_1^*\L\psi_2 d\tau=\int (\L\psi_1)^*\psi_2 d\tau[/tex]
[tex]\int \psi_1^*A^t\psi_2 d\tau=\int (A\psi_1)^*\psi_2 d\tau[/tex]
The Attempt at a Solution
[tex]\int \psi_1^*i(A-A^t)\psi_2 d\tau[/tex]
[tex]=\int \psi_1^*iA\psi_2 d\tau + \int \psi_1^*(-iA^t)\psi_2 d\tau[/tex]
[tex]=\int (iA^t\psi_1)^*\psi_2 d\tau + \int ((-iA)\psi_1)^*\psi_2 d\tau[/tex]
[tex]=\int i((A-A^t)\psi_1)^*\psi_2 d\tau[/tex]
Is this right? The signs are wrong in the third line, but taking the i out of the complex conjugate brackets fix them. Can I do that?
Last edited: