Question

1) Consider the Orbital Angular Momentum Operator ???? defined by: ? L?x = yp?z - zp?y ? L?y = zp?x - xp?z ? L?z = xp?y - yp?x Using the commutation relations: [x, p?x] = [y, p?y] = [z, p?z] = i?, [x, p?y] = [y, p?z] = [z, p?x] = ... = i? and [x, y] = [y, z] = [p?x, p?y] = ... = [p?y, p?z] ... = 0 Show that the components of ???? satisfy: [L?x, L?y] = i? L?z

          1) Consider the Orbital Angular Momentum Operator ???? defined by:
? L?x = yp?z - zp?y
? L?y = zp?x - xp?z
? L?z = xp?y - yp?x
Using the commutation relations:
[x, p?x] = [y, p?y] = [z, p?z] = i?,
[x, p?y] = [y, p?z] = [z, p?x] = ... = i?
and [x, y] = [y, z] = [p?x, p?y] = ... = [p?y, p?z] ... = 0
Show that the components of ???? satisfy:
[L?x, L?y] = i? L?z

1) Consider the Orbital Angular Momentum Operator ???? defined by:
? L?x = yp?z - zp?y
? L?y = zp?x - xp?z
? L?z = xp?y - yp?x
Using the commutation relations:
[x, p?x] = [y, p?y] = [z, p?z] = i?,
[x, p?y] = [y, p?z] = [z, p?x] = ... = i?
and [x, y] = [y, z] = [p?x, p?y] = ... = [p?y, p?z] ... = 0
Show that the components of ???? satisfy:
[L?x, L?y] = i? L?z

Added by Raymond M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Arjun Singh

02/24/2022

Step 1

The commutator of two operators A and B is defined as [A,B] = AB - BA. So, [Lx,Ly] = LxLy - LyLx. Substituting the given expressions for Lx and Ly, we get: [Lx,Ly] = (2px - ypx)(ypx - 2py) - (ypx - 2py)(2px - ypx). Expanding this out, we get: [Lx,Ly] = Show more…

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Consider the Orbital Angular Momentum Operator L defined by: Lx = ypz - zpy, Ly = zpx - xpz, Lz = xpy - ypx. Using the commutation relations: [x, px] = [y, py] = [z, pz] = iℏ, [x, py] = [y, pz] = [z, px] = ... = iℏ and [x, y] = [y, z] = [px, py] = [py, pz] ... = 0 Show that the components of L satisfy: [Lx, Ly] = iℏ Lz.