Given the initial state, Ican find the time evolution wave function right?

[cks]

Homework Statement

At t=0, the particle is in the eigenstate S_x, which corresponds to the eigenvalues -\hbar \over 2The particle is in a magnetic field and its Hamiltonian is H=\frac{eB}{mc}S_z. Find the state at t>0.

Homework Equations

Eigenstate of the Sx is

|->_x=\frac{1}{2^\frac{1}{2}}(|+>-|->)

The Attempt at a Solution

Since I am given with the initial state, then

|-(t)>_x=\frac{1}{2^\frac{1}{2}}(e^\frac{-iE_+t}{\hbar}|+>-e^\frac{-iE_-t}{\hbar}|->)

where E_t=\frac{eB}{mc}

and E_-=-\frac{eB}{mc}

Why am I wrong?

 

[nrqed]

Homework Statement

At t=0, the particle is in the eigenstate S_x, which corresponds to the eigenvalues -\hbar \over 2The particle is in a magnetic field and its Hamiltonian is H=\frac{eB}{mc}S_z. Find the state at t>0.

Homework Equations

Eigenstate of the Sx is

|->_x=\frac{1}{2^\frac{1}{2}}(|+>-|->)

The Attempt at a Solution

Since I am given with the initial state, then

|-(t)>_x=\frac{1}{2^\frac{1}{2}}(e^\frac{-iE_+t}{\hbar}|+>-e^\frac{-iE_-t}{\hbar}|->)

where E_t=\frac{eB}{mc}

and E_-=-\frac{eB}{mc}

Why am I wrong?

Looks right to me except for a factor of hbar/2 missing in your energies.

 

[cks]

yaya, aisheah, thank you very much. why I always miss something!