What is the significance of generalized angular momentum in quantum mechanics?

[snoopies622]

I'm looking at McMahon's Quantum Mechanics Demystified and in the angular momentum chapter he introduces "generalized" angular momentum J, which is the sum of a particle's orbital angular momentum and its spin.

It seems strange to me that these two things can be simply added together. Isn't "spin" only an indication of a subatomic particle's built in magnetic moment, completely unrelated to angular momentum in a classical sense?

 

[jtbell]

No, "spin" really is angular momentum. Changes in "spin" orientation of a large number of electrons in an object can affect macroscopic rotational motion, similarly to the way you can change your rotational motion while sitting on a rotating stool by holding a spinning wheel in your hands and "flipping" it over. See the Einstein-de Haas effect:

http://www.ptb.de/en/publikationen/jahresberichte/jb2005/nachrdjahres/s23e.html

https://www.physicsforums.com/showthread.php?t=58810

I still remember thinking "wow!" when I first read about this in the Feynman Lectures on Physics about forty years ago.

 

[01030312]

Spin and classical angular momentum are parts of a grand scheme known as "representation of rotation group". Its just classical angular momentum we see usually since classical angular momentum is that part of "representation of rotation group" that acts on vectors.

 

[Dadface]

No, "spin" really is angular momentum. Changes in "spin" orientation of a large number of electrons in an object can affect macroscopic rotational motion, similarly to the way you can change your rotational motion while sitting on a rotating stool by holding a spinning wheel in your hands and "flipping" it over. See the Einstein-de Haas effect:

http://www.ptb.de/en/publikationen/jahresberichte/jb2005/nachrdjahres/s23e.html

https://www.physicsforums.com/showthread.php?t=58810

I still remember thinking "wow!" when I first read about this in the Feynman Lectures on Physics about forty years ago.

That is interesting and brought back an ancient memory of a discovery made by a friend whilst fiddling around with a strong magnet .He suspended a knife from its point from the magnet and then spun the knife.It spun,slowed down and eventually stopped,which was no surprise,but then it started spinning for a while in the opposite direction which was a surprise.

 

[snoopies622]

Hey, thanks. Can electron orbital angular momentum also be made noticable on a macroscopic scale?

 

[snoopies622]

Just thought I'd give this a bump before it slips over the horizon. I'm hoping someone knows the answer to my follow-up question in box #5 above. Thanks.

 

[Drakkith]

Hrmm. I'm not sure snoopies. I know Spintronics deals with issue like that in order to put them to use in semiconductors thought.

 

[snoopies622]

..otherwise, how do we know that it really represents angular momentum as well?

 

[Drakkith]

I believe we can measure it at.