## Localization of the states of a $$PT$$-symmetric double well.(English)Zbl 1329.81168

Summary: We make a nodal analysis of the processes of level crossings in a model of quantum mechanics with a $$PT$$-symmetric double well. We prove the existence of infinite crossings with their selection rules. At the crossing, before the PT-symmetry breaking and the localization, we have a total P-symmetry breaking of the states.

### MSC:

 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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### References:

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