# Potential wells

## Homework Statement

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.

## Homework Equations

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)
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?

Related Advanced Physics Homework Help News on Phys.org
Dick
Homework Helper
Things started to break down when you evaluated the derivatives. Why is there a k1 on the left side? And why didn't the i's cancel out in the final solution?

siddharth
Homework Helper
Gold Member
ik1(A-B) = -ik2C/k1
Apart from the extra k1 on the left side which Dick pointed out, why is there a minus sign on the right side?

sorry should the differentials be (A-B)=-ik2C/k1?
in which case i still get the same solutions for A and B and a coefficient of 1

siddharth
Homework Helper
Gold Member
Why is there a minus sign on the left hand side?