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
How can I determine the values of α and β for a canonical transformation?
Reply to thread
Message
[QUOTE="Steve4Physics, post: 6845369, member: 681522"] Hi [USER=696125]@Lambda96[/USER]. I’m no expert, but (since you haven’t any other replies and I may have seen where you are going wrong) here goes... What you have written suggests that you are trying to apply a general format to construct equations for systems with 2 or more degrees of freedom. But the problem is simpler than that. The given transformation equations (for ##p’## and ##q’##) show the system has only one degree of freedom (so the phase space is 2-dimensional). That means ##\vec x## has only two components, ##x_1 = q## and ##x_2 = p##. Similarly ##\vec x’## has only two components, ##x_1’= q’## and ##x_2’ = p’##. The Jacobian tranformation matrix,##J##, is 2x2. For example ##J_{11} = \frac {∂x_1’}{∂x_1} = \frac {∂q’}{∂q}## Since ##q’ = \sqrt 2 p^α \sin q ## then ##J_{11} = \frac {∂q’}{∂q}= \sqrt 2 p^ α \cos q## Similarly, you need to find ##J_{12}, J_{21}## and ##J_{22}##. The corresponding symplectic identity matrix, ##I##, is also a 2x2 matrix (the elements are simple integers). You are dealing only with 2x2 matrices (but still probably have some messy working ahead!). Multiply-out ##JIJ^T## and then find what values of ##\alpha## and ##\beta## are needed to make ##JIJ^T=I##. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Advanced Physics Homework Help
How can I determine the values of α and β for a canonical transformation?
Back
Top