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!

Integral with symmetric infinitesimal bounds

  1. Oct 25, 2015 #1
    1. The problem statement, all variables and given/known data
    I'm reading something in my quantum physics book that says given a wavefunction ψ that is even, if we evaluate its integral from -ε to ε, the integral is 0. How can this be? I thought this is the property of odd functions.

    2. Relevant equations
    ψ=Aekx if x<0 and ψ=Be-kx if x>0, ε is infinitesimal change in x

    3. The attempt at a solution
    By boundary conditions, say at the origin, this will give A=B then the book says we can represent the wave function as ψ=Ae-k|x|. The wave function is even so the integral is 0 between -ε to ε.
     
  2. jcsd
  3. Oct 25, 2015 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    That is false. For very small, but positive ##\epsilon## the function ##\psi(x)## is very nearly constant (##=A##) over the interval ##-\epsilon \leq x \leq \epsilon##, so ##\int_{-\epsilon}^{\epsilon} \psi(x) \, dx \approx 2 A \epsilon##. Of course, if ##\epsilon## is infinitesimal, so is the integral, but infinitesimal does not mean zero.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Integral with symmetric infinitesimal bounds
  1. Bounded integral (Replies: 2)

  2. Integral bounds (Replies: 2)

  3. Integral Bounds (Replies: 8)

Loading...