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- Homework Statement
- Consider a a system described by the following Hamiltonian:

H=(L^2)/2I -gBLy

where I is a momentum of Inertia, B is the y-component of a uniform magnetic field while finally g is a constant.

At t=0, a measurement of L^2 and Lz gives, respectively 2h^2 and 0 as results.

Under these hypotheses determine:

1) The state of the system at a generic time t;

2) The mean values of the energy and of Lx;

3) The minimal time at which the state of the system is an eigenstate of Lx.

(Hint: Remember that Lx and Ly are a combination of Ladder Operators L+ and L-).

- Relevant Equations
- Lx = 1/2(L+ + L-)

Ly=-i/2(L+ - L-)

I think that the quantum numbers are l=1 and ml=0, so I write the spherical harmonic Y=Squareroot(3/4pi)*cos(theta).

I would like to know how to compute the wave function at t=0, then I know it evolves with the time-evolution operator U(t), to answer the first request.

I would like to know how to compute the wave function at t=0, then I know it evolves with the time-evolution operator U(t), to answer the first request.