The linear PT-Symmetric complex potential

Abstract : The spectrum of a PT-symmetric complex-valued linear potential is investigated. Working in the D = 1 dimensional space, we consider V(x) = λ|x| + icx. Semianalytical solutions are given by using the properties of the Airy functions. The numerical integration of the differential equation system is discussed. We show that the number of eigenstates with a real eigenvalue is limited, depending on the ratio c/λ and on the quantum number n. This is reflecting the spontaneous breaking of PT symmetry. For the ground state, we conjecture the eigenvalue to be real for any value of c.
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R. Lombard, R. Mezhoud. The linear PT-Symmetric complex potential. Romanian Journal of Physics, 2017. ⟨in2p3-01997748⟩

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