Introduction

Jan Nesemann

A chapter in PT-Symmetric Schrödinger Operators with Unbounded Potentials, 2011, pp 1-7 from Springer

Abstract: Abstract In the theory of quantum mechanics the Hamiltonian H is typically selfadjoint, i.e., H = H*. The self-adjointness ensures that the spectrum of the Hamiltonian, representing the energy spectrum of H, is real but it is not a necessary condition. In the literature on so-called PT-symmetric quantum mechanics (see, e.g., [BB98], [BBM99], [BBJ03], [Ben04b] and [Ben07]), it is believed that self-adjointness is rather a mathematical requirement than a physically established fact. Therefore, it was considered a surprise that operators exist which are not self-adjoint in the given quantum mechanical Hilbert space, but have real spectrum and that – if e.g. complex eigenvalues were present – they occurred only in complex conjugate pairs.

Date: 2011
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DOI: 10.1007/978-3-8348-8327-8_1

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