 |
Center for Nonlinear Studies |
In quantum mechanics the Schrödinger equation is a differential equation whose solutions give the possible energy levels of the system and their associated eigenfunctions. In the standard formulation a technical condition, Hermiticity, is imposed on the equation, so as to ensure that the energy levels are real. It has recently been realized that this condition can be relaxed somewhat, and there exists a whole class of systems with complex potentials which nonetheless have real energy eigenvalues. We show how this works at the level of differential equations for a soluble toy model, and for a much more interesting model, the “upside down” quartic oscillator.
Host: Carl Bender, T-CNLS