- #1
microsansfil
- 325
- 43
Hi all,
What is the link between noncommuting observables
[tex]{\displaystyle [{\hat {A}},{\hat {B}}]={\hat {A}}{\hat {B}}-{\hat {B}}{\hat {A}} \neq 0}[/tex]
and indeterminacy principle (which is about inequality relation of standard deviation of the expectation value of observables A and B ) ?
If the observables commute we can find a complete set of simultaneous eigenvectors if not this implies that no quantum state can simultaneously be both A and B eigenstate. Why this implies that we cannot measure one without affecting statisticaly the other (uncertainty principle) ?
Is it possible to measure simultaneously the two incompatibles observables knowing that when a state is measured, it is projected onto an eigenstate in the basis of the relevant observable ?
best regards
Patrick
What is the link between noncommuting observables
[tex]{\displaystyle [{\hat {A}},{\hat {B}}]={\hat {A}}{\hat {B}}-{\hat {B}}{\hat {A}} \neq 0}[/tex]
and indeterminacy principle (which is about inequality relation of standard deviation of the expectation value of observables A and B ) ?
If the observables commute we can find a complete set of simultaneous eigenvectors if not this implies that no quantum state can simultaneously be both A and B eigenstate. Why this implies that we cannot measure one without affecting statisticaly the other (uncertainty principle) ?
Is it possible to measure simultaneously the two incompatibles observables knowing that when a state is measured, it is projected onto an eigenstate in the basis of the relevant observable ?
best regards
Patrick