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!

Separating Schrodinger's Equation

  1. Aug 17, 2003 #1
    I'm looking for the mathematical demonstration that the Time Dependent Schrodinger Equation can be separated into time-independent Schrodinger equation and time evolution equation.

    Does anybody know a link which such demonstration?
    Last edited by a moderator: Aug 17, 2003
  2. jcsd
  3. Aug 17, 2003 #2


    User Avatar
    Science Advisor
    Gold Member


    iħ ∂Ψ/∂t = - ħ2/2m ∂2Ψ/∂x2 + VΨ

    Okay now assuming energy is conserved (i.e. a closed sytsem)and thus V is time-independant:

    Ψ(x,t) = u(x)T(t)

    subsituting that into the TDSE:

    iħ 1/T dT/dt = - 1/u ħ2/2m d2u/dx2

    The left hand side is noe independent of x and the right is now independant of t, yet this equation must hold true for all values of x and t therfore:

    iħ dT/dt = ET

    Where E is a constant, thus:

    - ħ/2m d2u/dx2 + V(x)u = Eu
  4. Aug 17, 2003 #3
    Thank you, very very much!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook