What Are the Permissible (L,S) Pairs for J=1 in a System of Two Spin-1 Bosons?

In summary, the conversation discusses a system of 2 indistinguishable spin-1 bosons in the center of mass frame. The total spin, relative orbital angular momentum, and total angular momentum are defined as S, L, and J respectively. It is required to prove that J equals 2m, where m is an integer. The permissible (L,S) pairs for J=1 are also requested. The Bose-Einstein statistics are mentioned, and it is noted that the overall wavefunction should be symmetric under the interchange of the 2 bosons. However, the speaker is unsure of how even and odd wavefunctions for orbital angular momentum behave. The significance of choosing the center of mass frame is also questioned. After some discussion,
  • #1
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Homework Statement



We have a system of 2 indistinguishable spin-1 bosons. We shall adopt the center of mass frame.

Let
S = total spin
L = relative orbital angular momentum
J = L+S = total angular momentum

Prove that J = 2m where m is an integer.
If given that J=1, what are the permissible (L,S) pairs?

Homework Equations


Bose-Einstein Stats?

The Attempt at a Solution


I am lost with this. I have managed to show that for the states S=0, S=2 interchanging particles 1,2 is symmetric, whereas it is antisymmetric for S=1. However, I don't know how to use this here.
What is the significance of the CoM frame choice?
Also, due to Bose-Einstein stats, the overall wavefunction should be symmetric under the interchange of the 2 bosons. However, I don't know how even and odd wavefunctions for orbital angular momentum behave. Anyone please?
 
Last edited:
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No worries. Problem resolved. Thanks for reading anyways.
 

FAQ: What Are the Permissible (L,S) Pairs for J=1 in a System of Two Spin-1 Bosons?

What is spin angular momentum?

Spin angular momentum is a fundamental property of particles, such as electrons and protons, that describes their rotation around their own axis. It is quantized, meaning it can only have certain discrete values, and is measured in units of Planck's constant divided by 2π.

How does spin angular momentum differ from orbital angular momentum?

Orbital angular momentum refers to the rotational motion of a particle around a point or axis, while spin angular momentum refers to the internal rotation of a particle. Orbital angular momentum is determined by the position and velocity of a particle, while spin angular momentum is an intrinsic property of the particle.

What is the relationship between spin and magnetic moments?

Spin and magnetic moments are closely related, as the spin of a particle creates a magnetic moment. In quantum mechanics, this magnetic moment is described as the interaction between the spin of a particle and an external magnetic field. The magnitude of the magnetic moment is proportional to the particle's spin.

Can spin and orbital angular momentum be changed?

Both spin and orbital angular momentum are conserved quantities, meaning they cannot be created or destroyed. However, they can be transferred between particles through interactions, such as collisions or electromagnetic fields.

How does spin angular momentum impact the behavior of particles?

The spin of a particle plays a crucial role in determining its properties and behavior. For example, particles with half-integer spin, such as electrons, are subject to the Pauli exclusion principle, which restricts the number of particles that can occupy a certain energy state. Spin also affects the magnetic properties and interactions of particles.

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