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Question: a what are the conditions on the energy of the...

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Part II: Longer problems. You must show your work to receive credit. tationary states. 35 points. A particle is moving in the

a) What are the conditions on the energy of the particle E for it to be in a bound state? In a scattering state?

b) Write down the time-independent Schrödinger equation in regions II and III.

For the rest of the problem, consider only the bound-state solutions.

c) Identify and clearly define the wave number (k or kappa) in regions II and III. Make sure that the waye number is real.

d) Write down the general form of the wave function psi(x) in regions I, II, III.

e) Write down the complete set of boundary conditions on the wave function psi(x).

f) Apply the boundary conditions on psi to eliminate and/or relate the unknown coefficients A,B, etc. and to obtain a transcendental equation that relates the wave numbers ​​​​​​​in regions II and III.

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