Isospectral hermitian counterpart of complex nonhermitian Hamiltonian p2- gx4 + a/x2

Abstract

We show that the nonhermitian Hamiltonians H = p2-gx4 + a/x2 and the conventional hermitian Hamiltonians h = p2 + 4gx4 + bx (a, b) are isospectral if a = (b2-4g 2)/16g and a ≥-2/4. This new class includes the equivalent nonhermitian-hermitian Hamiltonian pair, p2-gx4 and-2g x, found by Jones and Mateo six years ago as a special case. When a = (b2-4g2)/16g and a <-2/4 although h and H are still isospectral, b is pure imaginary, and h is no longer the hermitian counterpart of H.