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in $C^*-$algebras with unit element, there is the definition of a state, as a functional $\omega$ with $\omega(e)=||\omega||=1.$ Now, of course there is also in classical physics and quantum ...

$\DeclareMathOperator\tr{tr}$One begins with a quantum mechanical system, i.e. a unital $C^*$-algebra $A$. It is common to begin the discussion with embedding $A$ into the algebra of bounded operators ...

I'm trying to understand how bad things could possibly get without Cauchy completeness as a criterion for Hilbert spaces in quantum mechanics. Obviously, doing calculus on a pre-Hilbert space would be ...

Both physical and mathematical theories of quantum scattering seem to be well developed in the case when the potential (or a more general perturbation of the Laplacian) decays fast enough at infinity ...

Let $\mathscr{H}$ be a complex Hilbert space and $A$ be an Hermitian operator $A: \mathscr{H}\to \mathscr{H}$. Suppose, for a moment, that $A$ has a set of discrete eigenvalues $\{\lambda_{n}\}_{n\in \...