# Equations of motion of two-level systems %%Under what regime are these equations? This may only be if there is a uniform external field%% $i\hbar\dot{c}_g=c_e(t)H_{ge}(t)(e^{i\omega t-i\omega_{eg}t}+e^{-i\omega t-i\omega_{eg}t})$ ^1dfc09 and $i\hbar\dot{c}_e=c_g(t)H_{ge}(t)(e^{i\omega t+i\omega_{eg}t}+e^{-i\omega t+i\omega_{eg}t})$ ^ca7bcc Under the [rotating wave approximation](rotating%20wave%20approximation.md) this pair of equations becomes $i\hbar\dot{c}_g=c_e(t)H_{ge}(t)(e^{i\omega t-i\omega_{eg}t})$ ^a06664 and $i\hbar\dot{c}_e=c_g(t)H_{ge}(t)(e^{-i\omega t+i\omega_{eg}t})$ ^e002a1 ## Bloch equations With these equations we can derive the [Bloch Equations](Bloch%20Equations.md). #QuantumMechanics/QuantumDynamics/TwoLevelSystems #QuantumMechanics/TwoLevelSystems