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!

Hilbert Space

  1. Oct 9, 2007 #1
    [SOLVED] Hilbert Space

    1. The problem statement, all variables and given/known data
    For What Values of [tex]\psi(x)=\frac{1}{x^{\alpha}}[/tex] belong in a Hilbert Sapce?


    2. Relevant equations
    [tex]\int x^{a}=\frac{1}{a+1} x^{a+1} [/tex]


    3. The attempt at a solution
    I tried to use the condition that function in Hilbert space should satisfy:
    [tex]\int\psi^{2}=A[/tex] but it seems always infinite exist in x=0 or x=infinite
     
    Last edited: Oct 9, 2007
  2. jcsd
  3. Oct 9, 2007 #2

    Gokul43201

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Why are you writing the integral of x^a, when you want to examine the integral of 1/x^{2a}?

    Also, have you written down the question completely? What is the domain on which [itex]\psi(x)[/itex] is defined?
     
  4. Oct 9, 2007 #3
    one is alpha and another is a. I just write a integral equation, a = 2*alpha. I think it is not the key point. The question is complete. I asked my professor if there is some constrain of x, she said x can be any value. that is to say the integral will from minus infinite to infinite
     
  5. Oct 9, 2007 #4

    Gokul43201

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Okay, they both looked the same to me.
    It can not be. There's at least a couple of missing words. Here's one way to write a somewhat more complete question:

    For what values of [itex]\alpha [/itex] does [itex]\psi(x)=1/{x^{\alpha}}[/itex] belong in a Hilbert space?

    This needs to be specified in the question. You have not completely specified a function unless you describe its domain.
     
  6. Oct 9, 2007 #5
    Thanks, I explained it in the interval of minus infinite to minus zero and zero to infinite. I guess a wave function with singularity is not a good one in physic....
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Hilbert Space
Loading...