Should Symmetric Quantum Mechanics Be Interpreted as Nonlinear?

Miloslav Znojil
2002 Journal of Nonlinear Mathematical Physics  
The Feshbach-type reduction of the Hilbert space to the physically most relevant "model" subspace is suggested as a means of a formal unification of the standard quantum mechanics with its recently proposed PT symmetric modification. The resulting "effective" Hamiltonians H(eff) are always Hermitian, and the two alternative forms of their energy-dependence are interpreted as a certain dynamical nonlinearity, responsible for the repulsion and/or attraction of the levels in the Hermitian and/or
more » ... symmetric cases, respectively. The spontaneous PT symmetry breaking is then reflected by the loss of the Hermiticity of H(eff) while the pseudo-unitary evolution law persists in the unreduced Hilbert space.
doi:10.2991/jnmp.2002.9.s2.11 fatcat:i7z3pugmlrdvfkyvtd6pqi3d6y