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
Eigenvalue for a Hamiltonian
Reply to thread
Message
[QUOTE="yuanyuan5220, post: 3631192, member: 99678"] [h2]Homework Statement [/h2] I am solving a Hamiltonian including a term \begin{equation}(x\cdot S)^2\end{equation} [h2]Homework Equations[/h2] The Hamiltonian is like this form: \begin{equation} H=L\cdot S+(x\cdot S)^2 \end{equation} where [B]L[/B] is angular momentum operator and [B]S[/B] is spin operator. The eigenvalue for \begin{equation}L^2 , S^2\end{equation} are \begin{equation}l(l+1), s(s+1)\end{equation} [h2]The Attempt at a Solution[/h2] If the Hamiltonian only has the first term, it is just spin orbital coupling and it is easy to solve. The total [B]J[/B]=[B]L[/B]+[B]S[/B], [B]L[/B][SUP]2[/SUP] and [B]S[/B][SUP]2[/SUP] are quantum number. However, when we consider the second term \begin{equation}(x\cdot S)^2\end{equation}, it becomes much harder. The total [B]J[/B] is still a quantum number. We have \begin{equation}[(x\cdot S)^2, J]=0\end{equation}. However, \begin{equation}[(x\cdot S)^2,L^2]≠0\end{equation} The [B]L[/B] is no long a quantum number anymore. Anybody have ideas on how to solve this Hamiltonian? [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Advanced Physics Homework Help
Eigenvalue for a Hamiltonian
Back
Top