Studying the linear complex PT symmetric potential

Abstract EN

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 dierential 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.