- #1

Spinnor

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## Main Question or Discussion Point

Say we have two particles of mass m which repel each other, V = V(seperation). Let these particles be constrained to move on a circle of radius r. The particles want to stay at opposite sides of the circle because they repel each other. We want to treat this as a quantum problem so the particles may tunnel past each other depending on how the particles repel each other at short distances. (Seems like this system could "vibrate", rotate, tunnel, and resonate? By varying the potential, mass, and circle diameter we might get interesting quantum states?)

What is the l = 1 angular momentum state of these two particles when they rotate together? Will it be L = [2]^.5hbar = 2mvr where v is the velocity of the particles?

v = [2]^.5hbar/2mr

If V is turned off and the particles no longer interact the l = 1 angular momentum state for each particle now L = [2]^.5hbar = mvr?

v = [2]^.5hbar/mr

Two interacting particles of mass m and velocity v on a circle is similar to a single particle of mass 2m and the same velocity v constrained to a circle as far as angular-momentum is concerned?

Can you say anything about the angular-momentum of a system of N mutually repelling particles of mass m constrained to move on a circle of radius r?

Thanks for any help!

What is the l = 1 angular momentum state of these two particles when they rotate together? Will it be L = [2]^.5hbar = 2mvr where v is the velocity of the particles?

v = [2]^.5hbar/2mr

If V is turned off and the particles no longer interact the l = 1 angular momentum state for each particle now L = [2]^.5hbar = mvr?

v = [2]^.5hbar/mr

Two interacting particles of mass m and velocity v on a circle is similar to a single particle of mass 2m and the same velocity v constrained to a circle as far as angular-momentum is concerned?

Can you say anything about the angular-momentum of a system of N mutually repelling particles of mass m constrained to move on a circle of radius r?

Thanks for any help!

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