Discussion
Which identity of the following does not hold true for Poisson bracket ?
(Where all the symbols have their usual meaning)
Answer: B
The identity that does not hold is \([L_{i}, L_{j}] = \delta_{ij}\).
The components of angular momentum do not have a Kronecker-delta bracket with each other; they form the rotation algebra:
\[ [L_{i}, L_{j}] = \epsilon_{ijk}L_{k} \]
In particular \([L_{i}, L_{i}] = 0\) for any single component, whereas \(\delta_{ii} = 1\), so the stated identity fails even for \(i = j\).
The other three are the standard results: \([x_{i}, p_{j}] = \delta_{ij}\) is the fundamental bracket, and \([L_{i}, p_{j}] = \epsilon_{ijk}p_{k}\) and \([x_{i}, L_{j}] = \epsilon_{ijk}x_{k}\) express that \(\vec{p}\) and \(\vec{r}\) transform as vectors under rotations.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development