The quantum energy eigenvalues near the separatrix energy are found by combination of previous analysis of the quantum states near a barrier top with recent results for the behavior of the classical action near a separatrix. It is found that the minimum energy separation vanishes only logarithmically with Planck's constant. As a result, quantum aspects of the states of a Penning trap should be observable.
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Cary et al. (1987) studied this question.
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