- #1
fog37
- 1,568
- 108
Hello,
Today I am studying complete set of commuting observables (CSCO) which is a set of commuting operators, pair by pair, whose eigenvalues completely specify the state of a system. For example, given 4 different commuting observables, there is a set of eigenstates which are eigenstates for all the four commuting operators but the eigenvalues are clearly different.
It is said that the state $$|\Psi>$$ is completely specified by those commuting observables. But what about those observables that do not commute? I am sure that, for a particular system, there may be other observables that do not commute.
Isn't the truly complete state $$|\Psi>$$ of the system represented by a unit vector state in the Hilbert vector space that is the tensor product of all the Hilbert vector subspaces with each subspace associated to a different observable? It seems that all observables would be truly needed to give the most complete description...
I am sure there is something to tweak/correct in my understanding since I do not see how a set containing a finite number of commuting observables could give the most complete description of the state...
Thanks!
Today I am studying complete set of commuting observables (CSCO) which is a set of commuting operators, pair by pair, whose eigenvalues completely specify the state of a system. For example, given 4 different commuting observables, there is a set of eigenstates which are eigenstates for all the four commuting operators but the eigenvalues are clearly different.
It is said that the state $$|\Psi>$$ is completely specified by those commuting observables. But what about those observables that do not commute? I am sure that, for a particular system, there may be other observables that do not commute.
Isn't the truly complete state $$|\Psi>$$ of the system represented by a unit vector state in the Hilbert vector space that is the tensor product of all the Hilbert vector subspaces with each subspace associated to a different observable? It seems that all observables would be truly needed to give the most complete description...
I am sure there is something to tweak/correct in my understanding since I do not see how a set containing a finite number of commuting observables could give the most complete description of the state...
Thanks!