It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one
that has a positive-definite spectrum and obeys the requirement of unitarity) must be …

The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and
bounded below. Replacing this condition by the weaker condition of PT symmetry, one …

The Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A
standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity …

Abstract Quasi-Exactly Solvable Schrödinger Equations occupy an intermediate place
between exactly-solvable (eg the harmonic oscillator and Coulomb problems, etc.) and non …

This chapter introduces the basic ideas of P T-symmetric systems. It begins with a brief
discussion of closed (isolated) and open (non-isolated) systems and explains that P T …

In most introductory courses on quantum mechanics one is taught that the Hamiltonian
operator must be Hermitian in order that the energy levels be real and that the theory be …

This paper reviews a recently discovered link between integrable quantum field theories and
certain ordinary differential equations in the complex domain. Along the way, aspects of …

Abstract Changes of coordinates represent one of the most effective ways of deriving
solvable potentials from ordinary differential equations for separate special functions. Here …

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The progress of the factorization method since the 1935 work of Dirac is briefly reviewed.
Though linked with older mathematical theories the factorization seems an autonomous' …