Angular momentum - integer or half-integer

In summary, the operators J, L, and S have eigenvalues j(j+1), l(l+1), and s(s+1) respectively. The orbital momentum L must have an integer value, while the total momentum J can have either an integer or half-integer value. The spin S can only take half-integer values. The value of j labels a particle species and can be either an integer or half-integer. The spin s of a specific particle can only change by integer amounts, and thus j must also be integer or half-integer. This is due to the one-valuedness of the wave function.
  • #1
paweld
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Let J be total angular momentum, L - orbital angular momentum and S - intristic momentum (spin). Squares of these operators have appropriate eigenvalues j(j+1), l(l+1), s(s+1). Which of these numbers j,l,s should be integer. I know that spin can have half-integer values. But probably orbital or total momentum values should be integer. Thanks for answer.
 
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  • #2
The orbital momentum value must be integer. It results from the wave function one-valuedness.
The total momentum value can be half-integer.
 
  • #3
j and s can both be half integer. j is one of the numbers that labels a particle species. The s of a specific particle can only change by integer amounts, and since the lowest possible value of s is always -j and the highest always +j, this means that j must be integer or half integer.

Examples: When j=1, s can take the values -1,0,1. When j=1/2, s can take the values -1/2,1/2.
 

1. Is angular momentum an integer or half-integer value?

Angular momentum can have both integer and half-integer values, depending on the system it is describing. In classical mechanics, angular momentum is typically an integer value, while in quantum mechanics it can have half-integer values.

2. How is angular momentum quantized?

In quantum mechanics, angular momentum is quantized, meaning it can only take on discrete values. This is due to the wave-like nature of particles and the restrictions of their motion within an atom. The quantization of angular momentum is a fundamental principle in quantum mechanics.

3. What is the difference between orbital and spin angular momentum?

Orbital angular momentum refers to the motion of a particle around a fixed point, such as the orbit of an electron around the nucleus of an atom. Spin angular momentum, on the other hand, refers to the intrinsic angular momentum of a particle, such as the spin of an electron around its own axis.

4. Can angular momentum change?

According to the law of conservation of angular momentum, the total angular momentum of a system remains constant unless acted upon by an external torque. This means that while the individual components of angular momentum (such as orbital and spin) can change, the total angular momentum of the system will remain constant.

5. How is angular momentum related to rotational motion?

Angular momentum is a measure of an object's rotational motion. It takes into account both the mass and velocity of an object as well as the distance from the axis of rotation. As the rotational motion of an object changes, so does its angular momentum.

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