1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What, really, is the Variational technique?

  1. Oct 17, 2015 #1
    I have come across mention of using 'the variational technique' for solving the 1-D Schrodinger (and I assume many more eqtns). I really don't understand what the variational technique is, not getting anywhere fast by googling, can someone walk me through the basics please? I gather it is used for solving ODEs for example ...

    I think it has to with the variational priciple which is (Wiki) 'general methods for finding functions which minimize or maximize the value of quantities that depend upon those functions'. An example (also from Wiki) goes: "What is the shape of a chain suspended at both ends?" - we can use the variational principle that the shape must minimize the gravitational potential energy.

    In other words it will hang down? Clearly it must be more interesting than this example suggests to me, would appreciate some insights & intuitions. Maybe even an example of a function that can be found to minimize values w.r.t. some well known function? Thanks
     
  2. jcsd
  3. Oct 18, 2015 #2

    ZapperZ

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Back up a bit.

    You went straight into variational technique for Schrodinger equation. Have you not done such a thing in classical mechanics first before jumping into quantum mechanics? Have you not done Lagrangian/Hamiltonian mechanics?

    Mary Boas's text "Mathematical Methods in the Physical Sciences" has a whole chapter on Calculus of Variation and the Least Action principle. That chapter alone is worth getting the book.

    Zz.
     
  4. Nov 7, 2015 #3
    I did my physics over 20 years ago, we didn't cover Lagrangian/Hamiltonian mechanics, it is on my to do list, but it's quite a hefty topic and I have course deadlines .....

    I've kind of given up work to study, so funds ...... could someone point me at an online resource - a nice 'for dummies' type starter?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What, really, is the Variational technique?
  1. What really is sky? (Replies: 3)

  2. What is really green ? (Replies: 102)

Loading...