Ad Hoc Physical Hilbert Spaces in Quantum Mechanics

FRANCISCO M. FERNÁNDEZ; JAVIER GARCIA; IVETA SEMORÁDOVÁ; MILOSLAV ZNOJIL

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS

SPRINGER/PLENUM PUBLISHERS

Lugar: New York; Año: 2014

0020-7748

The overall principles of what is now widely known as PT-symmetric quantummechanics are listed, explained and illustrated via a few examples. In particular, modelsbased on an elementary local interaction V(x) are discussed as motivated by the naturallyemergent possibility of an efficient regularization of an otherwise unacceptable presenceof a strongly singular repulsive core in the origin. The emphasis is put on the construc-tive aspects of the models. Besides the overall outline of the formalism we show howthe low-lying energies of bound states may be found in closed form in certain dynamicalregimes. Finally, once these energies are found real we explain that in spite of a manifestnon-Hermiticity of the Hamiltonian the time-evolution of the system becomes unitary in aproperly amended physical Hilbert space.