View Full Version : Separating Schrodinger's Equation...
MiCasilla
Aug17-03, 02:34 AM
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?
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
MiCasilla
Aug17-03, 01:10 PM
Thank you, very very much!
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