Raising and lowering operators acting on spin 1 kets?

In summary, raising and lowering operators are mathematical operators used in quantum mechanics to describe the behavior of particles with spin. They change the spin quantum number by one unit and are important in the study of angular momentum and particle creation and annihilation. They are related to the spin angular momentum operator and can be applied to particles with any spin value.
  • #1
philip041
107
0
I read in my notes that

S{-}|1> = sqrt(2)h(bar)|0>

and similar for all six products of using the raising and lowering operators on |1>, |0>, |-1>

I don't understand where the sqrt(2)h(bar) has come from?

Cheers

Philip
 
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  • #2
[tex] J_{\pm}|j,m> = \hbar \sqrt{j(j+1) - m(m\pm 1 )}|j,m \pm 1 > [/tex]
 
  • #3
bo select
 
  • #4
philip041 said:
bo select

Huh?
 

1. What are raising and lowering operators in quantum mechanics?

Raising and lowering operators are mathematical operators used in quantum mechanics to describe the behavior of particles with spin. They act on quantum states, or kets, to change the spin quantum number by one unit.

2. How do raising and lowering operators act on spin 1 kets?

Raising and lowering operators act on spin 1 kets by changing the spin quantum number by one unit, either increasing or decreasing it. For example, if the spin quantum number is 1, the raising operator will increase it to 2, and the lowering operator will decrease it to 0.

3. What is the significance of raising and lowering operators in quantum mechanics?

Raising and lowering operators are important in quantum mechanics because they allow us to describe the behavior of particles with spin. They are also used in the study of angular momentum and in the creation and annihilation of particles.

4. How do raising and lowering operators relate to the spin angular momentum operator?

Raising and lowering operators are related to the spin angular momentum operator by the fact that they are eigenstates of the spin angular momentum operator. This means that when the spin angular momentum operator acts on a spin 1 ket, it will produce a multiple of the ket itself, which can be either the raising or lowering operator.

5. Are raising and lowering operators only applicable to spin 1 particles?

No, raising and lowering operators can be applied to particles with any spin, including spin 1/2, 1, 3/2, and so on. However, the specific form and properties of the operators may differ depending on the spin value of the particle.

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