Question

Consider a particle of mass m and energy E approaching the step potential?

V (x)= 0, x<0

V(x)=V0, x>0

from negative values of x. Consider the case E > V0. a) Classically, what is the probability of re?ection? b) Quantum mechanically, what is the probability of re?ection? Express your result in terms of the ratio V0/E. What is the probability of re?ection if E = 2V0?

Answer #1

If then the particle will not be reflected at all calssically. Hence the classical probability of reflection is R = 0

Quantum probability of reflection is

where

and

where

Therefore the quantum probability is

when

When a particle of energy E hits the boundary of a step
potential of potential V0>0 at x=0, when is the probability that
it will get reflected greater than 0 (that is, R>0)?
A.Always
B.Only if E>V0
C.Only if the potential step is positive (that is, V=0 for
x<0, V=V0 for x>0)
D.Only if the potential step is negative (that is, V=V0 for
x<0, V=0 for x>0)
E.Never
Only if E<V0

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