Given an Hilbert space $H$ (finite dimensional for sake of clarity), and two non-commuting operators $$A = \sum_a a |a\rangle\langle a|$$ and $$B=\sum_a b |b\rangle\langle b|,$$ is it possible to find ...
Why are the position and potential energy of a particle able to be measured precisely in Quantum Mechanics? I mean why do they commute with each other?
I've just been introduced to the idea of commutators and I'm aware that it's not a trivial thing if two operators $A$ and $B$ commute, i.e. if two Hermitian operators commute then the eigenvalues of ...
I'm now learning quantum mechanics with Liboff. In the book it deals with "a compete set of mutually compatible observables" in order to make a state maximally informative. How can one find such set? ...
I have searched for an answer to this question on physics SE but I have not seen a question in which it is addressed properly. Please let me know if there is an answer already. My question briefly ...
How does linearity of a measurement imply that the commutator of all measured observables are $c$-numbers?
I really don't understand with the linearity conditions I have where this comes from.
I'm studying Quantum Mechanics on my own, so I'm bound to have alot of wrong ideas - please be forgiving! Recently, I was thinking about the quantum mechanical assertion (postulate?) that states with ...
My QM book says that when two observables are compatible, then the order in which we carry out measurements is irrelevant. When you carry out a measurement corresponding to an operator $A$, the ...