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

Wave Function

  1. Jun 13, 2008 #1
    Hi everyone, Can any body solve my simple problems of quantum:
    Usually we say, that wave function Ψ is dependent on r,θ,Φ .But this is just a coordinate system,or more than that. Imagination to this is qite difficult.
    Moreover somewhere in a book I have read that if Ψ = f(r,θ) exp(imΦ),then on increment of 2pi in Φ does not change wave function.? Why?
  2. jcsd
  3. Jun 13, 2008 #2
    Did you mean to ask the question: "Is this just a coordinate system,or more than that?"
    If so, then it looks like you are just presenting spherical coordinates. Instead of your axes defining three edges of a box (as in Cartesian coordinates), your three axes define a sphere.

    This just means that the specific wavefunction you have is sinusoidally periodic in Φ.
  4. Jun 13, 2008 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You can think of points in space as something independent of coordinates, and coordinate systems as functions that assign three numbers to each point in space. If p is a point in space and f and g are coordinate systems, then

    [tex]\psi(p)=(\psi\circ f^{-1})(f(p))=(\psi\circ g^{-1})(g(p))[/tex]

    If f assigns the cartesian coordinates and g the spherical coordinates, then we can write [itex](\psi\circ f^{-1})(x,y,z)=(\psi\circ g^{-1})(r,\theta,\phi)[/itex].

    So you can think of your wave function as the composition of a coordinate independent wave function and the inverse of a coordinate system.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook