- #1

oddiseas

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## Homework Statement

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.

## Homework Equations

## 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;