Learning Goal D=0 · To understand the qualities of the finite square-well potent

Question

Learning Goal D=0 · To understand the qualities of the finite square-well potential and how to connect solutions to the Schrödinger equation from different regions Submit My Answers Give Up The case of a particle in an infinite potential well, also known as the particle in a box, is one of the simplest in quantum mechanics. The closely related finite potential well is substantially more complicated to solve, but it also shows more of the qualities that are characteristic of quantum systems. The potential energy function for a finite square-well potential is Correct Again, you see that the wave function is nonzero throughout the entire classically forbidden region. 0, 0KL, Part C Recall that a physical solution to the Schrödinger equation must be continuous everywhere. Consider the two branches Cekt where Uo is a positive number that measures the depth of the potential well and L is the width of the well. (Figure 1) The figure is a graph of potential energy versus position, which shows why this is called the square-well potential. Inside the well (i.e., for 0

Explanation / Answer

C. given

for x < 0, psi(x) = Ce^kx

for x > 0, psi(x) = Acos(kx) + Bsin(kx)

at x = 0

from LHS

psi(x) = C

from RHS

psi(x) = A

hence

for continuity

A = C

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