Answer:
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Step-by-step explanation:
In the atomic system of units, the normalized states - spin vectors of a particle with a specified projection sy = ±1/2 on the y-axis can be calculated using the following steps:
1. Start with the spin state vector notation: |sy⟩.
2. Normalize the state vector by dividing it by the square root of 2: |sy⟩ / √2.
3. Since the projection can be either +1/2 or -1/2, we can write the normalized states as:
For sy = +1/2: |+1/2⟩ = |sy⟩ / √2
For sy = -1/2: |-1/2⟩ = |sy⟩ / √2
4. Simplify the expression by substituting the value of |sy⟩ with the y-component basis vector: |+1/2⟩ = |y+⟩ / √2 and |-1/2⟩ = |y-⟩ / √2.
So, in the atomic system of units, the normalized states - spin vectors with a specified projection sy = ±1/2 on the y-axis are:
For sy = +1/2: |+1/2⟩ = |y+⟩ / √2
For sy = -1/2: |-1/2⟩ = |y-⟩ / √2
These vectors represent the possible spin states of a particle along the y-axis, with the specified projections. The normalization ensures that the total probability of finding the particle in any spin state is 1.