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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

    jcsd

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    okay:


    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!
     
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