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Studying The Linear Complex Pt Symmetric Potential, Roland Lombard
Studying The Linear Complex Pt Symmetric Potential, Roland Lombard
Journal of the Arab American University مجلة الجامعة العربية الامريكية للبحوث
We investigate the spectrum of the linear complex PT symmetric potential V(x) = λ|x| + icx. Semi analytical solutions are given by using 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, reflecting a spontaneous breaking of the PT symmetry. For the ground state ( n = 0), we conjecture the eigenvalue to be real whatever the value of c.