A particle with the velocity v and the probability currentdensity J is incident from the left on a potential step of height Uo, that is,U (x) = Uo at r > 0 and U(x) = 0 at r < 0. The particle has the energyE < Uo and thus gets fully reflected by the step. Calculate the probabilitydensity w(x) to find the particle in the classically-forbidden region r> 0.

Solution: To calculate the probability density to find the particle in the classically-forbidden…

A particle with the velocity v and the probability current density J is incident from the left on a potential step of height Uo, that is, U (r) Uo at r > 0 and U(r) = 0 at r < 0. The particle has the energy E < Uo and thus gets fully reflected by the step. Calculate the probability density w(x) to find the particle in the classically-forbidden region r> 0.

A particle with the velocity v and the probability current density J is incident from the left on a potential step of height Uo, that is, U (r) Uo at r > 0 and U(r) = 0 at r < 0. The particle has the energy E < Uo and thus gets fully reflected by the step. Calculate the probability density w(x) to find the particle in the classically-forbidden region r> 0.