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 $$-\hbar \over 2$$The 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 $$-\hbar \over 2$$The 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!