Answer to Question #145708 in Quantum Mechanics for Viccy

Question #145708

Write down Lx is term linear angular momentum.


1
Expert's answer
2020-11-25T10:54:30-0500

In classical mechanics :

"L = r\\times p"

Therefore to pass to quantum mechanics we just replace the physical quantities by the corresponding operators (and sometimes by "hermitianizing" the result). In "r" representation we have :

"\\hat{L} = \\hat{r}\\times\\hat{p}=-i\\hbar \\hat{r}\\times\\vec{\\nabla}"

And so we have

"\\hat{L}_x=-i\\hbar (y\\frac{\\partial}{\\partial z} - z\\frac{\\partial}{\\partial y}" )

We can verify that the obtained result is an observable (a hermitian operator).


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