Orbital Angular Momentum: Need at least 2 particles?

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Orbital angular momentum is defined as the cross product of position and momentum (rxp), allowing for a single particle to possess it around a defined origin. However, practical examples of a one-particle system exhibiting orbital angular momentum are elusive, suggesting that at least two particles are typically necessary. When considering a single particle, moving the reference frame to the particle's position effectively nullifies its orbital angular momentum. In contrast, systems with two or more particles maintain an "absolute" angular momentum that cannot be disregarded by changing the reference frame. Thus, while one-particle systems can theoretically have orbital angular momentum, it is often impractical to consider them in isolation.
LarryS
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The definition of orbital angular momentum, whether for classical mechanics or for quantum mechanical operators, is rxp. Technically, according to this definition, one particle can possesses orbital angular momentum - in this case about the origin.

But I cannot think of any examples, in classical or quantum mechanics, in nature in which a system of one particle has orbital angular momentum. It seems like a minimum of 2 "particles" is necessary.

Comments?

As always, thanks in advance.
 
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Every system of one particle has "orbital" angular momentum - in some frames.
It's just pointless to consider those reference frames if you really just have one particle. It is much more convenient to put the origin of your reference frame where the particle is.
 
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mfb said:
Every system of one particle has "orbital" angular momentum - in some frames.
It's just pointless to consider those reference frames if you really just have one particle. It is much more convenient to put the origin of your reference frame where the particle is.

Makes sense. If one has a system of just 1 particle, then you can make the system's angular momentum "go away" by moving the origin of the reference frame to the position of the particle. But, obviously, you cannot do that if the system contains 2 or more particles. It's like those system's angular momentum are "absolute".
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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