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Draw the PIB wavefunctions for 1,3-butadiene.

##### Solution Summary

A few qualitative problems based on expectation value, eigenvalue, PIB functions for 1,3-butadiene are included.

##### Solution Preview

1. If  is an eigenfunction of the operator A, then every measurement of that property yields only 1 result - the eigenvalue of . The expectation value, being the mean value, is obviously that same value. If, however,  is not an eigenfunction of A, then any given measurement will produce a result which is an eigenvalue of A. However, the average value over many measurements (the expectation value) is a weighted sum of the eigenvalues of A, the weighting factor being the square modulus of the coefficients in the expansion.
Any experiment can only give a single result - the pointer on our "observable detect-o-meter" can only point to one value. THESE VALUES CAN ONLY EVER BE AN EIGENVALUE OF THE OPERATOR. The average of many measurements, however, will correspond to the expectation value for that ...

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