Could the function ψ(x)=Asin(π*x/L) for 0≤x≤L and ψ(x)=0 elsewhere (where A and L are real and positive constants) possibly be a valid quanton wavefunction under the right circumstances? Why or why not? (Hint: Sketching a graph of this wavefunction and its absolute square might prove helpful.)

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter29: Atomic Physics
Section: Chapter Questions
Problem 60P
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Could the function ψ(x)=Asin(π*x/L) for 0≤x≤L and ψ(x)=0 elsewhere (where A and L are real and positive constants) possibly be a valid quanton wavefunction under the right circumstances? Why or why not? (Hint: Sketching a graph of this wavefunction and its absolute square might prove helpful.)

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