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.

• Received 22 September 1986

DOI:https://doi.org/10.1103/PhysRevLett.58.292