Homework Statement
I want to show that
tr\left(\hat{\rho}_{mixed}\right)=1
tr\left(\hat{\rho}_{mixed}^{2}\right)<1
when
\hat{\rho}_{mixed}=\frac{1}{2\pi}\int_{0}^{2\pi}d \alpha \hat{\rho}(\psi)
Homework Equations
tr\left(\psi\right)= \sum_{n}\langle n|\psi|n\rangle...
Hello,
I am looking (searching :) ) for a possibility to use the AND operator, for example find all of the following words in the title of a subject in this forum:
integral density operator
integral AND density AND operator
+integral +density +operator. There is already a thread...
I found the solution here: http://books.google.de/books?id=0Yx5VzaMYm8C&pg=PA110&redir_esc=y#v=twopage&q&f=true .
That's Heinz-Peter Breuer, Petruccione, "The Theory of Open Quantum Systems", pp. 110-111.
Nearly every step ist explained.
The definition should be \hat{\rho}=\sum_{i}p_{n}|\psi(t)\rangle\langle\psi(t)|
I can do with that:
\partial_{t}\hat{\rho}=\partial_{t}\sum_{i}p_{n}| \psi(t)\rangle\langle\psi(t)|+ \sum_{i} p_{n}|\psi(t) \rangle\partial_{t}\langle\psi(t)| \Leftrightarrow...