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.
Relfection coefficient is given by R= (B*B)/(A*A)
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)
x>0 ((-hbar/2m)dphisquared/dphi +Vo phi = Ephi(x)
the solutions to this
x<0 Aexp(ik1x) +Bexp(-ik1x) = phi(x)
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
when I find R i get R=1 which must wrong because particle is not always reflected it should pass over the potential barrier?