[UPSC IFoS 2020] Schrodinger’s Wave equation and applications (Q148, 10+5=15M)

(i) Draw a neat sketch of a finite rectangular potential barrier well of height U' and width L' that contains a particle whose energy E' is less than U'. Solve the Schr"{o}dinger equations of the particles outside the well. (ii) Plot wave functions and probability densities |\psi|^2 of the particle for the first three states. Compare the results with that of a particle in a box of infinite potential (U = \infty).