Question

In three-dimensional systems, for cases where the potential depends only on the ra- dial position in spherical coordinates, the Hamiltonian is given in the following form and possesses rotational symmetry. $H = \frac{P^2}{2m} + V(r)$ Given the angular momentum operator $L_x$, show that $[H, L_x] = 0$ (Hint: Consider the rotation around the x-axis only.

          In three-dimensional systems, for cases where the potential depends only on the ra-
dial position in spherical coordinates, the Hamiltonian is given in the following form
and possesses rotational symmetry.
$H = \frac{P^2}{2m} + V(r)$
Given the angular momentum operator $L_x$, show that $[H, L_x] = 0$
(Hint: Consider the rotation around the x-axis only.

In three-dimensional systems, for cases where the potential depends only on the ra-
dial position in spherical coordinates, the Hamiltonian is given in the following form
and possesses rotational symmetry.
H = (P^2)/(2m) + V(r)
Given the angular momentum operator Lx, show that [H, Lx] = 0
(Hint: Consider the rotation around the x-axis only.

Added by Michael W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

07/14/2023

Step 1

Step 1: We need to calculate the commutator [H, L] and show that it equals zero. Show more…

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In three-dimensional systems,for cases where the potential depends only on the ra- dial position in spherical coordinates,the Hamiltonian is given in the following form and possesses rotational symmetry p2 H= -+Vr) 2m Given the angular momentum operator L show that [H,L]=0 (Hint: Consider the rotation around the x-axis only.