0
votes
2answers
66 views

How can $J_1^2, J_2^2, J_{1z}, J_{2z}$ commute mutually?

I'm reading through J. J. Sakurai's Modern Quantum Mechanics book and currently looking at the "Angular-momentum addition" part. Here, it says you have two options and that one option is to ...
2
votes
1answer
151 views

The Physical Meaning behind a Commutator [duplicate]

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 ...
3
votes
3answers
220 views

Is commutation relation an equivalence relation?

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? ...
1
vote
0answers
59 views

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.
4
votes
3answers
3k views

Proof of Canonical Commutation Relation (CCR)

I am not sure how $QP-PQ =i\hbar$ where $P$ represent momentum and $Q$ represent position. $Q$ and $P$ are matrices. The question would be, how can $Q$ and $P$ be formulated as a matrix? Also, what is ...
3
votes
2answers
262 views

Why does $i ( LK-KL )$ represent a real quantity?

According to my textbook, it says that $i( LK-KL )$ represents a real quantity when $K$ and $L$ represent a real quantity. $K$ and $L$ are matrices. It says that this is because of basic rules. ...
1
vote
2answers
373 views

Symmetries, Generators, Commutators and Observables

I'm learning about generators and conservation laws and have derived the equation (1) $$[Q,A]=-i\hbar f(A)$$ which is satisfied by the observable generator $Q$ for a transformation group with ...
4
votes
1answer
2k views

Compatible Observables

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 ...
9
votes
5answers
10k views

What is the Physical Meaning of Commutation of Two Operators?

I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable ...