Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Classical Physics
Quantum Physics
Quantum Interpretations
Special and General Relativity
Atomic and Condensed Matter
Nuclear and Particle Physics
Beyond the Standard Model
Cosmology
Astronomy and Astrophysics
Other Physics Topics
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Classical Physics
Quantum Physics
Quantum Interpretations
Special and General Relativity
Atomic and Condensed Matter
Nuclear and Particle Physics
Beyond the Standard Model
Cosmology
Astronomy and Astrophysics
Other Physics Topics
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Physics
Quantum Physics
Expectation value in Heisenberg picture: creation and annihilation
Reply to thread
Message
[QUOTE="Bruno Cardin, post: 6643982, member: 702063"] [B]TL;DR Summary:[/B] Hi. I posted this in homework, but it isn't really homework. I'm just someone who has spent 2 years in classical general relativity and find myself lost trying to re-do my final exam. So, I have a hamiltonian for screening effect, written like: $$ H=\sum_{k}^{}\epsilon_{k}c_{k}^{\dagger}c_{k}+ \frac{1}{\Omega}\sum_{k,q}^{}V(q,t)c_{k+q}^{\dagger}c_{k} $$ And I have to find an equation for the time evolution of the expected value of the operator ##c_{k-Q}^{\dagger}c_{k}##. I wrote this, initially $$ i\hbar\frac{d}{dt}c_{k-Q}^{\dagger}(t)c_{k}(t)= [c_{k-Q}^{\dagger}c_{k} , H] $$ as the time evolution equation for the operator in the Heisenberg picture. What I procceed to do is to plug a bra in the left <phi| and a ket in the right |phi> , with phi being an energy eigenstate, and then start raising and lowering energy levels since the operators ##c_{k}## are the anihilation operators (and with the dagger they switch to creation operators). But the result I have to get to, according to the exam's solution is: $$ i\hbar\frac{d}{dt} < c_{k-Q}^{\dagger}(t)c_{k}(t) > = (\epsilon_{k}-\epsilon_{Q-k})< c_{k-Q}^{\dagger}c_{k}>+\frac{1}{\Omega}\sum_{k}^{}V(q,t)[<c_{k-Q}^{\dagger}c_{k-q} >- <c_{k+q-Q}^{\dagger}c_{k}>]$$ which has the expression of V in it.. this means I have to "open" the hamiltonian. I'm so rusty that that didn't even cross my mind. I don't get it. Could anyone help? Thank you in advance. [/QUOTE]
Insert quotes…
Post reply
Forums
Physics
Quantum Physics
Expectation value in Heisenberg picture: creation and annihilation
Back
Top