Two-level system

A two-level system is a quantum mechanics system in which there are two physical states of different energy. That is, if we take the time-independent Hamiltonian to be $H$ , then we say that the two levels are $ψ a$ and $ψ b$ with corresponding energy eigenvalues $E a$ and $E b$ , which may or may not be different. These states are always taken to be orthonormal, i.e. $\left\langle\psi_a|\psi_b\right\rangle=\delta_{ab}.$ If the system is initialized in the state $\Psi(t=0)=c_a\left.|\psi_a\right\rangle+c_b\left.|\psi_b\right\rangle$ then after evolving for some time $t$ under the Hamiltonian $H$ , the state will be $\Psi(t) = c_a e^{-i\frac{E_at}{\hbar}}\left|\psi_a\right\rangle+ c_b e^{-i\frac{E_bt}{\hbar}}\left|\psi_b\right\rangle$

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Two-level system

See also: Two-level system, Eigenvalue, Hamiltonian, Physics, Quantum mechanical