(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A potential well with V(x)=0 for x<0 and V(x) = Vo for x>0. The particle has energy E greater than Vo and is incident from the left side. Calculate the reflection coefficient.

2. Relevant equations

Relfection coefficient is given by R= (B*B)/(A*A)

3. The attempt at a solution

I think that the time independent Schrodinger equation for the two regions are

x<0 (-hbar/2m)dphisquared/dphi =Ephi(x)

and

x>0 ((-hbar/2m)dphisquared/dphi +Vo phi = Ephi(x)

the solutions to this

x<0 Aexp(ik1x) +Bexp(-ik1x) = phi(x)

x>0 Cexp(ik2x)

is this right

carrying this through and equating two solutions at x=0

A+b = C

and equating differentials at x=0 gives

ik1(A-B) = -ik2C/k1

but when I solve for A and B i get

A=(c/2)(1-ik2/k1)

B=(c/2)(1+ik2/k1)

when I find R i get R=1 which must wrong because particle is not always reflected it should pass over the potential barrier?

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# Homework Help: Potential wells

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