Incompatible observables

  • Thread starter kakarukeys
  • Start date
190
0
Incompatible observables do not share a complete set of common eigenfunctions, because their operators do not commute.

It seems that, incompatible observables like x and p_x, S_x and S_y do not have any common eigenfunction at all.

Can anyone give a concrete example of a pair of incompatble observables that have common eigenfunctions but incomplete (do not span the Hilbert Space)?
 

Tom Mattson

Staff Emeritus
Science Advisor
Gold Member
5,475
20
kakarukeys said:
Can anyone give a concrete example of a pair of incompatble observables that have common eigenfunctions but incomplete (do not span the Hilbert Space)?
The only example I can think of is the state of zero orbital angular momentum. The eigenfunction common to the incompatible operators Lx, Ly, and Lz is the spherical harmonic Y00, with a zero eigenvalue.
 

Related Threads for: Incompatible observables

Replies
8
Views
2K
  • Posted
Replies
19
Views
3K
Replies
0
Views
1K
Replies
20
Views
2K
Replies
1
Views
1K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top