Scattering off PT-symmetric upside-down potentials
  The upside-down $-x^4$, $-x^6$, and $-x^8$ potentials with appropriate PT-symmetric boundary conditions have real, positive, and discrete quantum-mechanical spectra. This paper proposes a straightforward macroscopic quantum-mechanical scattering experiment in which one can observe and measure these bound-state energies directly. 
Carl M. Bender and Mariagiovanna Gianfreda
quant-ph hep-th math-ph math.MP