Non-Selfadjoint Opertors in Quantum Physics: Mathematical Aspects

0458004 - ÚJF 2016 US eng M - Monography Chapter
Krejčiřík, David - Siegl, Petr
Elements of Spectral Theory without the Spectral Theorem.
Non-Selfadjoint Opertors in Quantum Physics: Mathematical Aspects. Vol. 1. New Jersey: John Wiley & Sons, Inc., 2015, s. 233-282. ISBN 978-1-118-85528-7
Institutional support: RVO:61389005
Keywords : Hilbert Spaces * operators * theorem
Subject RIV: BE - Theoretical Physics

Many physical systems can be described by partial differential equations and the latter can often be viewed as generating abstract operators between Banach spaces. A typical example is quantum mechanics where the traditional mathematical discipline is the functional analysis of self-adjoint operators in Hilbert spaces. There are also effective models (typically describing open quantum systems, including non-real fields or complex boundary conditions) or more generally non-conservative processes in Nature on the whole where the underlying operator is non-self-adjoint. More intrinsically, there have been recent attempts to build quantum mechanics with physical observables represented by non-self-adjoint operators.
Permanent Link: http://hdl.handle.net/11104/0258324