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Lcarning Goal: Submit My Answers Glve Up To understand the qualities of the finite square-well potential and how to connect solutions to the Schrödinger equation from different regions. Correct 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 Part D The derivative must also be continuous everywhere to have a physical solution (unless there are points where the potential energy suddenly becomes infinite, which never happens for the finite square well). Take the derivative of the two branches that you looked at in Part C to find the value of B Express your answer in terms of k, , and C 0, 0<*SL, U(x) = 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 L) the solutions take the form $(z) = A cos kx + Bsin kT, where A and B are constants and k = V2mE/h. Outside the well, the solutions take the form ψ(z) = CeKZ + De-KZ, where C and D are constants and Submit My Answers Give Up Part E Figure 1 of 1 This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Part G

Answer 1

D) B = C k / K

E)

	D'e-L   = Acos (KL) + Asin (kL)

F) Zero

G)

	En   = 2 1 L2.2nn. (nr)

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