**Quantum Mechanics: Reflection at a Potential Step**Consider a particle with velocity \( v \) and probability current density \( J \) approaching a potential step from the left. The potential step has a height \( U_0 \), defined as:- \( U(x) = U_0 \) for \( x > 0 \)- \( U(x) = 0 \) for \( x < 0 \)The particle has an energy \( E \) such that \( E < U_0 \). Consequently, the particle is entirely reflected by the potential step.**Task:**Calculate the probability density \( w(x) \) that describes finding the particle in the classically forbidden region where \( x > 0 \).

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.

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.