Rotation Invariant of Sch. Equation and [Lx,H]=0] ?

[torehan]

Rotation Invariant of Sch. Equation and [Lx,H]=0] ??

Here is my first post,

How can I prove that the rotation invariability of the Sch. equations?

How can I prove that [Lx,H]=0

 

[samalkhaiat]

Here is my first post,

How can I prove that the rotation invariability of the Sch. equations?

How can I prove that [Lx,H]=0

Theorem: Schrödinger equation is invariant under O(3)-rotation if and only if;

$$x_{i} \partial_{k}V(x) = x_{k} \partial_{i}V(x)$$

Proof

$$\left[ L_{i} , H \right] = \epsilon_{ijk} \left[x_{j}p_{k} , p^{2} + V(x) \right] = \epsilon_{ijk}x_{j} \left[ p_{k} , V(x) \right]$$

Ok, you finish off the proof.

sam