1. Not finding help here? Sign up for a free 30min 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!

A simple differential equation!

  1. Mar 29, 2008 #1
    Just out of pure curiosity, can anyone here give me any advice on the problem of solving the following differential equation

    [tex]\left\{\sum_i \vec{\alpha}_i \cdot \nabla_i + \sum_{i neq j}\beta_{ij}\delta(x_i -x_j)\delta(\tau_i - \tau_j) \right\}\vec{\psi} = K\frac{\partial}{\partial t}\vec{\psi} = iKm\vec{\psi}.[/tex]


    [tex][\alpha_{ix} , \alpha_{jx}] \equiv \alpha_{ix} \alpha_{jx} + \alpha_{jx}\alpha_{ix} = \delta_{ij}[/tex]

    [tex][\alpha_{i\tau} , \alpha_{j\tau}] = \delta_{ij}[/tex]

    [tex][\beta_{ij} , \beta_{kl}] = \delta_{ik}\delta_{jl}[/tex]

    [tex][\alpha_{ix}, \beta_{kl}]=[\alpha_{i\tau}, \beta_{kl}] = 0 \text{ where } \delta_{ij} =
    \left\{\begin{array}{ c c }
    0, & \text{ if } i \neq j \\
    1, & \text{ if } i=j
    \end{array} \right.

    Any advice on approaching this problem would be greatly appreciated.

    Thank you very much!
  2. jcsd
  3. Mar 30, 2008 #2
    It doesn't look simple to me ...lol...
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: A simple differential equation!