- #1
mudyos
- 10
- 0
in the quantum mechanical operators :
why :
[YPz,YPx]=0
[ZPy,ZPy]=0
[X,Py]=0
[Y,Pz]=0
[Z,Py]=0
why :
[YPz,YPx]=0
[ZPy,ZPy]=0
[X,Py]=0
[Y,Pz]=0
[Z,Py]=0
Can you prove that [X Px] = i h ?
pellman said:Isn't [X Px] = i h an axiom, CompuChip?
The commutator of two operators in quantum mechanics represents the order in which they act on a state. When the commutator equals 0, it means that the operators can be applied in either order without changing the result. In the case of [YPz,YPx] and [ZPy,ZPy], this indicates that the momentum operators in the y and z directions are independent of each other.
Similar to the first question, when the commutator equals 0, it means that the operators can be applied in any order without changing the result. In this case, it indicates that the position operator and the momentum operator in the y direction are independent of each other.
As mentioned before, a commutator of 0 indicates that the operators can be applied in any order without changing the result. In this case, it means that the position and momentum operators in the y direction are compatible and can be measured simultaneously without affecting each other's values.
The uncertainty principle in quantum mechanics states that certain pairs of observables, such as position and momentum, cannot be known simultaneously with perfect precision. The commutators discussed above are related to this principle because they show that the operators for these observables do not commute, meaning that their values cannot be simultaneously determined with complete precision.
No, these specific commutators are not always equal to 0. It depends on the operators being considered. However, the commutators of certain pairs of operators, such as position and momentum, will always equal 0 due to the fundamental principles of quantum mechanics.