EffectiveHamiltonian

EffectiveHamiltonian[h, u, t]
returns the effective Hamiltonian corresponding to the Hamiltonian h under a (possibly time dependent) transformation u, assuming time variable t.
  • EffectiveHamiltonian finds the operator that satisfies the Schrödinger equation in the frame determined by the transformation matrix, even if that frame is non-inertial.
  • The formula for the effective Hamiltonian is .
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Define a system with Zeeman structure:
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Find the Hamiltonian assuming a single optical field of frequency :
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Find a unitary transformation for performing the rotating-wave approximation using RotatingWaveTransformMatrix:
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This matrix can be supplied to the function EffectiveHamiltonian to transform the Hamiltonian to the rotating frame without dropping the fast-oscillating terms:
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