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!

Homework Help: Kramers equation

  1. Apr 4, 2008 #1
    1. The problem statement, all variables and given/known data
    2. Relevant equations

    Find a solution to the PDE
    [tex] B P_{vv} - v P_x + (A v - F(x)) P_v + A P = 0 [/tex]
    where A and B are constants, P = P(x,v)

    3. The attempt at a solution

    I have no idea how to even guess a solution to this.
  2. jcsd
  3. Apr 4, 2008 #2
    I would suggest separation of variables, but that F(x) seems to screw things up a bit...
  4. Apr 5, 2008 #3
    Assumeing [tex]F(x) = -V_x[/tex] and makeing an ansatz
    [tex] P(x,v) = C_1 exp(C_2 x + C_3 V(x) + C_4 v + C_5 v^2) [/tex]
    I get these conditions on the constants C_i
    in the second eq we can put C_3=-2C_5 and get rid of F(x) there, but it's still in the third eq. Suggestions?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook