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!

Hamiltonian and Lagrangian

  1. Apr 12, 2015 #1
    "The hamiltonian runs over the time axis while the lagrangian runs over the trajectory of the moving particle, the t'-axis."
    What does the above statement means? Isnt hamiltonian just an operator that corresponds to total energy of a system? How is hamiltonian related to lagrangian intuitively?

    Besides what is lagrangian density intuitively and mathematically? Is it equal to lagrangian?
     
  2. jcsd
  3. Apr 12, 2015 #2

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  4. Apr 13, 2015 #3
  5. Apr 13, 2015 #4

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In the future, it's best to provide a reference to a quote so that folks can easily look at the source and context of the quote.
    I had to do a Google search and guessed this was the source.

    Concerning the statement of the quote...
    The interpretation doesn't seem to be a standard interpretation... but it seems interesting and might be worthy of further study.
    I can't say I understand enough of that interpretation to give a summary of the idea. (Do a search for ... hans de vries largrangian ).

    Since you refer to the Hamiltonian as an operator, your context seems to be quantum mechanics or quantum field theory, which appears to be the context of the quote. (See Ch 22 of the document that comes up in the Google search.)

    In classical mechanics, the Hamiltonian and Lagrangian are related by a Legendre Transformation.
    I don't have yet an "intuitive" explanation of that relationship... beyond saying it's an important transformation of variables. (part of a backburner project)

    While the largrangian is used in particle mechanics (with few degrees of freedom),
    the Lagrangian density is used in field theory (with many more degrees of freedom).
    Rather than being a function of configurations and velocities,
    it is a function of the field values and their derivatives in some region of space.
    Crudely speaking, the Lagrangian density is in some sense the Lagrangian-per-unit-volume.

    Possibly useful:
    http://en.wikipedia.org/wiki/Lagrangian
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Hamiltonian and Lagrangian
  1. Hamiltonian Principle (Replies: 1)

  2. Hamiltonian value (Replies: 4)

Loading...