2011 | OriginalPaper | Buchkapitel
Spectrum and Dynamics
verfasst von : Stephen J. Gustafson, Israel Michael Sigal
Erschienen in: Mathematical Concepts of Quantum Mechanics
Verlag: Springer Berlin Heidelberg
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Given a quantum observable (a self-adjoint operator)
A
, what are the possible values
A
can take in various states of the system? The interpretation of
〈 Ψ,AΨ 〉
as mean value of the observable
A
in a state
AΨ
, which is validated by quantum experiments, leads to the answer. It is the spectrum of
A
. The most important observable is the energy – the Schrödinger operator,
H
, of a system. Hence the spectrum of
H
gives the possible values of the energy.