An Equivalent Hermitian Hamiltonian for the non-Hermitian − x 4 Potential

@inproceedings{Jones2006AnEH,
  title={An Equivalent Hermitian Hamiltonian for the non-Hermitian − x 4 Potential},
  author={H W Francis Jones},
  year={2006}
}
The potential −x4, which is unbounded below on the real line, can give rise to a well-posed bound state problem when x is taken on a contour in the lower-half complex plane. It is then PT -symmetric rather than Hermitian. Nonetheless it has been shown numerically to have a real spectrum, and a proof of reality, involving the correspondence between ordinary differential equations and integral systems, was subsequently constructed for the general class of potentials −(ix)N . For PT -symmetric but… CONTINUE READING