Timeline for Quantum Probability, what makes quantum characteristic functions quantum?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 2, 2020 at 9:52 | comment | added | ACuriousMind♦ | @jgerber When you say "Why can I not interpret this as an expectation value?", then what do you mean by that? What does it mean for you to say that something is an expectation value? | |
| Feb 2, 2020 at 5:34 | comment | added | lcv | @AcuriousMind you could say exactly the same thing in the classical case as that expectation value is complex in that case (and no measurable quantity is). | |
| Feb 2, 2020 at 2:21 | comment | added | Jagerber48 | And so what if the expectation value of a random variable gives a complex number? Let's expand our scope in the classical case to allow complex valued random variables. | |
| Feb 2, 2020 at 2:21 | comment | added | Jagerber48 | Ok, but I can still calculate $\langle e^{i(t_Q Q + t_P P)} \rangle = \langle \psi| e^{i(t_Q Q + t_P P)}|\psi\rangle$. If the operator in the brackets were self-adjoint, $\langle H \rangle$ you would then say it is an observable so that we can let $E[H] = \langle H \rangle$. Let's just say this is my definition for $E\left[e^{i(t_Q Q + t_P P)}\right]$. Why can I not interpret this as an expectation value? Interpreted this way it leads to something we could call a characteristic function or a quasi-characteristic function. Why is it not a normal characteristic function? | |
| Feb 2, 2020 at 2:16 | history | answered | ACuriousMind♦ | CC BY-SA 4.0 |