Expectation value in a linear superposition

[solas99]

In a linear superposition, what is the relationship between expectation value of, say, energy and the amplitude coefficients of the eigenfunctions?

 

[Ken G]

That depends on what it is a superposition of. Normally, if you want to know the expectation value of some observable, you express the superposition in terms of "eigenfunctions" of that observable, meaning a superposition of states of a definite value for that observation. When you do that, the expectation value is a weighted average of those values, where the weights are the squared magnitude of the coefficients of the superposition.

 

[solas99]

thank you :)