- #1
SemM
Gold Member
- 195
- 13
Hi, I have the two operators:
\begin{equation}
Q = i\hbar \frac{d}{dx} - \gamma
\end{equation}\begin{equation}
Q' = -i\hbar \frac{d}{dx} - \gamma
\end{equation}
where ##\gamma## is a constant. Both of these are not self-adjoint, as they do not follow the condition:
\begin{equation}
\langle {Q}x, y \rangle = \langle x, {Q}^{*}y \rangle,
\end{equation}
thus being non-Hermitian.
This gives , for the system ##QQ' = 0## a non-selfadjoint solution, which cannot be normalized, or used to derive expectation values.
What can I do?
Thanks!
\begin{equation}
Q = i\hbar \frac{d}{dx} - \gamma
\end{equation}\begin{equation}
Q' = -i\hbar \frac{d}{dx} - \gamma
\end{equation}
where ##\gamma## is a constant. Both of these are not self-adjoint, as they do not follow the condition:
\begin{equation}
\langle {Q}x, y \rangle = \langle x, {Q}^{*}y \rangle,
\end{equation}
thus being non-Hermitian.
This gives , for the system ##QQ' = 0## a non-selfadjoint solution, which cannot be normalized, or used to derive expectation values.
What can I do?
Thanks!
Last edited: