Quantum Computation Magnetic Spin

[Jamestoomer]

Homework Statement

A qubit is in the state |ψ(0)>=|0> . A magnetic field is applied in the x^ direction at t=0. This corresponds to the Hamiltonian H=BX, where B is a constant and X is the usual bit flip gate. What are the coordinates (θ,ϕ) of this qubit on the Bloch sphere at time t, as a function of B and t?

Homework Equations

I think i have to introduce e^(-i*H*t) into the qubit state.
The generic form of |ψ (t)> = cos(θ/2)|0> + (e^(iϕ))*sin(θ/2)|1>

The Attempt at a Solution

I have followed this through and have got θ = ∏ and ϕ = B*t
However looking at the Bloch sphere it would seem that theta is ∏/2. Also from the diagram i would think that ϕ would be 0 or 2BT but i am not sure.

 

[NateD]

Any help would be greatly appreciated. A:If you've worked out that $\theta=\pi$ and $\phi=Bt$, then the coordinates of the qubit on the Bloch sphere are $(\frac{\pi}{2}, Bt)$. The $\theta$ coordinate is the angle from the north pole on the Bloch sphere, so it must be $\frac{\pi}{2}$.