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Homework Help: Schrodingers equation

  1. Dec 24, 2009 #1
    1. The problem statement, all variables and given/known data

    At t=0 a particle is described by the eigenfunction:

    [tex]\Psi[/tex]= i[tex] M [/tex] [tex]e^{\frac{-x}{2}}[/tex] x [tex]\geq 0[/tex]
    0 if x [tex]\prec 0[/tex]

    a) Write an expression for the corresponding wave function

    b) find the epression for the eigenfunctions.



    2. Relevant equations



    3. The attempt at a solution

    Does the wavefunction always approach zero as x approaches infinity?

    if so this gives me:
    f(x)=Be^ikx+Ce^-ikx
    f(0)=Aie^(-x/2)
    f([tex]\infty[/tex])=0 then B=0
    f(x)=Aie^(-x/2)e^-ikx

    f(x)=Aie^-x(ik+1/2)

    then normalising this solution gives A=[tex]\sqrt{2}[/tex]

    f[tex]_{n}[/tex](x)=[tex]\sqrt{2}[/tex]ie^-x(ik+1/2)

    then normalising the initial condition give M=1.

    [tex]\Psi[/tex]= [tex]\sum[/tex] A*[tex]\sqrt{2}[/tex]ie^-x(ik+1/2)*g(t)

    This is as far as i could get;
     
  2. jcsd
  3. Dec 24, 2009 #2
    With this eigenfunction, yes. [itex]\lim_{x\rightarrow\infty}\exp(-x)=0[/itex]
     
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