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 psi_a and psi_b with corresponding energy eigenvalues E_a and E_b, which may or may not be different.

Related Topics:
Quantum mechanics - Hamiltonian - Eigenvalue

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These states are always taken to be orthonormal, i.e.

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leftlanglepsi_a|psi_b ight angle=delta_{ab}.

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If the system is initialized in the state

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Psi(t=0)=c_aleft.|psi_a ight angle+c_bleft.|psi_b ight angle

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then after evolving for some time t under the Hamiltonian H,

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the state will be

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Psi(t) = c_a e^{-irac{E_at}{hbar}}left|psi_a ight angle+

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c_b e^{-irac{E_bt}{hbar}}left|psi_b ight angle

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