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*0<x<a*.

a)Construct a wave function

*phi(x)=psi(x,t=0)*such that when an energy measurement is made on the particle in this state at

*t=0*, the following energy values are obtained with the probabilities shown:

Energy E_n Obtained : E_1 E_3 E_5

Probability of Obtaining E_n : 0.5 0.4 0.1

b) Is this answer unique? Why or why not? Illustrate with an example.