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Topic: QM: Angular momentum operator & Commutation  (Read 9672 times)

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Offline Winga

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QM: Angular momentum operator & Commutation
« on: November 09, 2005, 02:16:33 PM »
How to show that
(J cap) x (J cap) = i(h bar)(J cap)

Is this a cross product or (J cap)2?
« Last Edit: November 09, 2005, 03:58:58 PM by Winga »
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Offline Winga

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Re:QM: Angular momentum operator & Commutation
« Reply #1 on: November 09, 2005, 04:10:04 PM »
Commutation:
Key: J = J cap, h = h bar

Show that
[Jx,Jy] = ihJz or [Lx,Ly] = ihLz

[Jx,Jy] = y[Pz,z]Px + x[Pz,z]Py
= y(-ih)Px + x(ih)Py
= ih(xPy - yPx)
= ihJz

My question is that why [Pz,z] is equal to -ih?


« Last Edit: November 10, 2005, 05:47:54 AM by Winga »
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Offline Winga

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Re:QM: Angular momentum operator & Commutation
« Reply #2 on: November 10, 2005, 05:42:16 AM »
I have solved the 1st question. ;D


About the 2nd question, actually, I don't know how this method that I posted derived from , I just followed the steps to do it.

I use another method (just calculate JxJy - JyJx), finally, all them terms are cancelled out.
Did I miss something?
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Offline Winga

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Re:QM: Angular momentum operator & Commutation
« Reply #3 on: November 10, 2005, 05:53:40 AM »
According to a reference book, there are 2 terms that I missed are x?/?y and y?/?x.
But I don' know how this 2 terms come from JxJy - JyJx.
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Offline Winga

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Re:QM: Angular momentum operator & Commutation
« Reply #4 on: November 10, 2005, 10:52:08 AM »
How this 2 terms (circled in blue) derived from?
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Offline Winga

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Re:QM: Angular momentum operator & Commutation
« Reply #5 on: November 14, 2005, 11:41:01 AM »
I have solved it.
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Offline Donaldson Tan

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Re:QM: Angular momentum operator & Commutation
« Reply #6 on: November 14, 2005, 08:12:27 PM »
 :thmbup: :thmbup: :thmbup:
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"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006
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