Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How do I write taylor expansion as exponential function?

  1. May 1, 2015 #1
    How do I write taylor expansion of a function of x,y,z (not at origin) as an exponential function?
    Please see the attached image. I need help with the cross terms. I don't know how to include them in the exponential function?
     

    Attached Files:

  2. jcsd
  3. May 1, 2015 #2

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, [itex]f(x+y) = f(x) + y \frac{d}{dx} f + \frac{y^2}{2} \frac{d^2}{dx^2} f + ...[/itex], which can be formally written as:

    [itex]f(x+y) = e^{y \frac{\partial}{\partial x}} f(x)[/itex]

    or to be more physics-like,

    [itex]f(x+y) = e^{\frac{i}{\hbar} y p_x} f(x)[/itex]

    This is discussed here:
    http://en.wikipedia.org/wiki/Translation_operator_(quantum_mechanics)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How do I write taylor expansion as exponential function?
Loading...