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!

Complex wave function

  1. Feb 12, 2009 #1
    Show that for ψ1 , ψ2 ∈ C,
    |ψ1 + ψ2 |^2
    can take any value in [0, 4α], where
    α = |ψ1 |^2 = |ψ2 |^ 2

    I think the solution has something to do with triangular identies but I am not sure how to start this problem at all.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 13, 2009 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I think you can get away without using the triangle inequality. If [itex]\psi_1[/itex] and [itex]\psi_2[/itex] both have constant modulus [itex]\sqrt{a}[/itex] then the functions must be of the following form (assuming 1 spatial dimension and time independence).

    [tex]\psi_1(x)=\sqrt{a}\exp\left(ik_1x+i\phi_1\right)[/tex]

    [tex]\psi_1(x)=\sqrt{a}\exp\left(ik_2x+i\phi_2\right)[/tex]

    Here [itex]k_1,k_2,\phi_1,\phi_2\in\mathbb{R}[/itex].

    Can you do something with that?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Complex wave function
  1. Complex function ? (Replies: 7)

  2. Wave function (Replies: 3)

Loading...