Question

Problem 3: Rotating a spin state (3 parts , 15 point)
PART A (6 points possible)
Consider the |+⟩ state of a spin one-half particle (as usual |±⟩=|z;±⟩) and apply to it the rotation operator R that rotates states by an angle θ around the y axis. Write out the resulting state |Ψ1⟩ in terms of the basis states |±⟩. Do not discard any phase.

Enter 'phi' for ϕ, 'theta' for θ, 'ketp' for |+⟩ and 'ketm' for |−⟩ as needed.

|Ψ1⟩=




PART B (6 points possible)
To the resulting state |Ψ1⟩ apply the rotation operator R that rotates by an angle ϕ around the z axis. Write out the resulting state |Ψ2⟩ in terms of the basis states |±⟩. Do not discard any phase.

Enter 'phi' for ϕ, 'theta' for θ, 'ketp' for |+⟩ and 'ketm' for |−⟩ as needed.

|Ψ2⟩=




PART C (3 points possible)
How is |Ψ2⟩ related to the state |n;+⟩ where n is the unit vector pointing in the (θ,ϕ) direction?

Enter 'phi' for ϕ, 'theta' for θ, 'ketp' for |+⟩ and 'ketm' for |−⟩ as needed.

|Ψ2⟩=
- unanswered
|n;+⟩