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
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
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
Homework Help
Advanced Physics Homework Help
Time-dependent perturbation theory
Reply to thread
Message
[QUOTE="DrClaude, post: 5729342, member: 461323"] What you showed is that if the system is in state ##|u_1 \rangle## or ##|u_2 \rangle##, which are eigenstates of the Hamiltonian, then the system will stay forever in those states, which is what you would expect for a time-independent Hamiltonian. This is all fine in the abstract Dirac notation. But when you go to matrix-vector notation, you have to make a choice of basis. In the problem, it is stated the basis used is ##|1\rangle \rightarrow (1, 0)^T## and ##|2\rangle \rightarrow (0, 1)^T ##. It is in that basis that $$ \hat{H} \rightarrow \begin{pmatrix} E & U \\ U & E \end{pmatrix} $$ such that the matrix elements ##H_{1,2} = H_{2,1} = U##. Note that in terms of the notes you have posted, ##|1 \rangle## and ##|2 \rangle## are eigenstates of ##\hat{H}_0##, $$ \hat{H}_0 \rightarrow \begin{pmatrix} E & 0 \\ 0 & E \end{pmatrix} $$ and the coupling is given by $$ \hat{H}' \rightarrow \begin{pmatrix} 0 & U \\ U & 0 \end{pmatrix} $$ So you are working with eigenstates of the base Hamiltonian ##\hat{H}_0##. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Advanced Physics Homework Help
Time-dependent perturbation theory
Back
Top