1.A particle moving in the positive x-direction encounters afinite step-function potential of magnitude V, at x = 0 asillustrated.a.b.The energy of the particle is E > Vo-I.ii.III.iii.PHYS 2305Homework 7II.iii.The energy of the particle is E < Voi.iii.VVWrite the wavefunction for the particle inregion 1 (x < 0) and region 2 (x > 0).Identify terms as Pincident, reflected and transmitted-Apply boundary conditions to determine relationships between thewavefunction coefficients.Determine P(T) the probability of transmission and P(R) theprobability of reflection for the particle.Write the wavefunction for the particle in region 1 (x < 0) andregion 2 (x > 0).Identify terms as incident, reflected and transmitted-Apply boundary conditions to determine relationships between thewavefunction coefficients.Determine P(T) the probability of transmission and P(R) theprobability of reflection for the particle.X

Solution: a. i. The schrodinger wave equatin is given by the following, d2ψdx2+2m♄2E-Vψ=0In the…

1. A particle moving in the positive x-direction encounters a finite step-function potential of magnitude V, at x = 0 as illustrated. a. The energy of the particle is E > V₁. i. ii. Write the wavefunction for the particle in region 1 (x < 0) and region 2 (x > 0). Identify terms as incident, reflected and transmitted- V. Vo x

1. A particle moving in the positive x-direction encounters a finite step-function potential of magnitude V, at x = 0 as illustrated. a. The energy of the particle is E > V₁. i. ii. Write the wavefunction for the particle in region 1 (x < 0) and region 2 (x > 0). Identify terms as incident, reflected and transmitted- V. Vo x