Question

Question on the mathematics of QM

Answer 1

A function of an observable \(f(\widehat{\xi})\) is defined by its usual taylor series treating the operator as a number. i.e. for \(a \in \mathbb{C}\)
\[f(\widehat{\xi})=\sum_0^\infty\frac{f^{(i)}(a)}{n!}(\widehat{\xi}-a)^i \]This assures that if \(|\xi '\rangle\) is and eigenket of the observable then it is also an eigenket of its function in the following manner \[\widehat{\xi}|\xi '\rangle=\xi'|\xi '\rangle \rightarrow f(\widehat{\xi})|\xi '\rangle=f(\xi')|\xi '\rangle \ \]If there is no taylor series the that is the definition of a function of an observable. How can we make sense of this in the case were the function of the observable is \[f(\widehat{q})=\frac{d}{dq}\]

Answer 2

DO NOT BELIEVE QUANTUM. IT IS NOT A COMPLETE THEORY OF THE WORLD.

Answer 3

@k142 Then what is? Classical physics?