Answered: Could the function Ψ(x)=Ax + B (where A…

Could the function Ψ(x)=Ax + B (where A and B are real constants) possibly be a valid wavefunction for a quanton under the right circumstances? Why or why not?

Stars and Galaxies (MindTap Course List)

10th Edition

ISBN:9781337399944

Author:Michael A. Seeds

Publisher:Michael A. Seeds

Chapter10: The Interstellar Medium

Section: Chapter Questions

Problem 8RQ

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Question

Could the function Ψ(x)=Ax + B (where A and B are real constants) possibly be a valid wavefunction for a quanton under the right circumstances? Why or why not?

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Suppose a quanton's wavefunction at a given time is y(x) = Asin(2πx/L) for - L≤ x L and y(x) = 0 everywhere else, where A is a scaling constant and L is a constant with untis of length. Suppose also the energy eigenfunction associated with the energy eigenvalue E is VE(x) = Bcos(лx/L) for - L≤x≤ ½ L and y(x) = 0 everywhere else, where B is a scaling constant. What is the probability that if we determine the quanton's energy, we get the result E? (Hint: Do not do an integral. Draw graphs of these functions and think about what the product of these function should look at. Recall that a function's integral delivers the area under that function's curve.)
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