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!

Superposition of wave functions

  1. Sep 6, 2010 #1
    If 2 particles have wave functions w1 and w2, in which W = w1 + w2 is a superposition of the wave functions, then would the probability density of W correspond to the probability of finding both particles at the same position within some interval of space?
     
    Last edited: Sep 6, 2010
  2. jcsd
  3. Sep 7, 2010 #2
    The short answer is yes. One of the postulates of quantum mechanics is

    "The state of any physical system is specified, at each time t, by a state vector [itex]|\psi(t) \rangle[/tex] in a Hilbert space, [itex]|\psi(t) \rangle[/tex] contains all the needed information about the system. Any superposition of state vectors is also a state vector."

    In fact, even further, that is exactly how finding the probability of a state works for discrete spectra. For nondegenerate discrete eigenvalues the probability of obtaining one of the eigenvalues [itex]a_n[/itex] of an operator [itex]\hat{A}[/itex] is given by

    [tex]P_n(a_n)=\frac{|\langle \psi_n | \psi \rangle|^2}{\langle \psi | \psi \rangle}[/tex]

    where [itex]\psi_n[/itex] is the eigenstate of [itex]\hat{A}[/itex] with eigenvalue a_n.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Superposition of wave functions
  1. Superposition of waves (Replies: 1)

  2. Wave superposition. (Replies: 3)

Loading...