Quantum Hamiltonian (Normal Mode, Anharmonic) (Q6674522)

quantum-mechanical represention of molecular normal modes of vibration beyond the harmonic approximation

Language	Label	Description	Also known as
English	Quantum Hamiltonian (Normal Mode, Anharmonic)	quantum-mechanical represention of molecular normal modes of vibration beyond the harmonic approximation

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\hat{H} = \frac{1}{2} \sum_{i = 1}^{3 N - 6} ω_{i} ({\hat{p}}_{i}^{2} + {\hat{q}}_{i}^{2}) + \frac{1}{6} \sum_{i j k} ϕ_{i j k} q_{i} q_{j} q_{k} + \frac{1}{24} \sum_{i j k l} ϕ_{i j k} q_{i} q_{j} q_{k} q_{l}

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N

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\hat{H}

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ω

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ϕ_{i j k l}

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ϕ_{i j k}

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p

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q

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