A free particle of mass m and kinetic energy E =3V0 is traveling to the right. At x = 0, the potential jumps from zero to V0 > 0, and remains at this value for positive x.
a) What is the wave number for the particle in the region of positive x?
b) Find the transmission coefficient T for this case.
c) Find the reflection coefficient R for this case.
d) If one million particles of mass m and kinetic energy E = 3V0 are incident upon this potential step, how many particle are expected to continue moving along the positive x direction? How does this evaluate with the classical prediction?