Quantum Mechanics: Foundations and Applications

Böhm, Arno

doi:10.1007/978-1-4612-4352-6

Cited by 331 publications

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“…(See Postulate Va of Bohm [4]. Postulate Vb is the Heisenberg form of the equation, and follows similarly.…”

Section: Dynamicsmentioning

confidence: 91%

“…It is now routine to define symmetric and anti-symmetric direct sums of σ-complexes, yielding the corresponding symmetric and anti-symmetric tensor products of Hilbert spaces, needed to deal with identical particles. (See Postulate IVb of Bohm [4]. The spin-statistics connection that Bohm adds can also be added here.…”

Section: Quantum Mechanics: σ-Complex Q = Q(h)mentioning

confidence: 99%

“…Here it appears as the unique answer to conditionalizing a state to a given property. (See Postulate IIIa of Bohm [4]. )…”

Section: Classcal Mechanics: σ-Algebra B(ω)mentioning

confidence: 99%

“…There are discussions in the literature on the conditions under which reduction can occur. For instance, Bohm [4] analyzes the strength of the inhomogeneity of the magnetic field for a successful reduction to occur in the Stern-Gerlach experiment. We consider these as interesting pragmatic questions which lie outside the purview of this paper.…”

Section: Introductionmentioning

confidence: 99%

“…We shall accordingly give only outlines of the proofs of the requisite theorems. To show that we have accomplished the goal of reconstructing the formalism, we shall use the textbook by Arno Bohm [4]. This book has the advantage of explicitly introducing five postulates which suffice to treat the standard topics in quantum theory.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Reconstruction of Quantum Mechanics

Kochen¹

2016

Quantum [Un]Speakables II

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“…(See Postulate Va of Bohm [4]. Postulate Vb is the Heisenberg form of the equation, and follows similarly.…”

Section: Dynamicsmentioning

confidence: 91%

Section: Quantum Mechanics: σ-Complex Q = Q(h)mentioning

confidence: 99%

“…Here it appears as the unique answer to conditionalizing a state to a given property. (See Postulate IIIa of Bohm [4]. )…”

Section: Classcal Mechanics: σ-Algebra B(ω)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Reconstruction of Quantum Mechanics

Kochen¹

2016

Quantum [Un]Speakables II

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Gamow dyads and expectation values

Gadella¹,

Laura

2001

Int. J. Quantum Chem.

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Rigged Hilbert Space Treatment of Continuous Spectrum

2002

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The ability of the Rigged Hilbert Space formalism to deal with continuous spectrum is demonstrated within the example of the square barrier potential. The non-square integrable solutions of the time-independent Schrödinger equation are used to define Dirac kets, which are (generalized) eigenvectors of the Hamiltonian. These Dirac kets are antilinear functionals over the space of physical wave functions. They are also basis vectors that expand any physical wave function in a Dirac basis vector expansion. It is shown that an acceptable physical wave function must fulfill stronger conditions than just square integrability-the space of physical wave functions is not the whole Hilbert space but rather a dense subspace of the Hilbert space. We construct the position and energy representations of the Rigged Hilbert Space generated by the square barrier potential Hamiltonian. We shall also construct the unitary operator that transforms from the position into the energy representation. We shall see that in the energy representation the Dirac kets act as the antilinear Schwartz delta functional. In constructing the Rigged Hilbert Space of the square barrier potential, we will find a systematic procedure to construct the Rigged Hilbert Space of a large class of spherically symmetric potentials. The example of the square barrier potential will also make apparent that the natural framework for the solutions of a Schrödinger operator with continuous spectrum is the Rigged Hilbert Space rather than just the Hilbert space.

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Quantum Mechanics: Foundations and Applications

Abstract: Library of Congress Cataloging in Publieation Data Bohm, Amo, 1936~ Quantum meehanies. (Texts and monographs in physies) Bibliography: p. Includes index. 1. Quantum theory. 1. Title. II. Series QCI74.12.B63 1986 530.1'2 85-4710

Cited by 331 publications

References 0 publications

A Reconstruction of Quantum Mechanics

A Reconstruction of Quantum Mechanics

Gamow dyads and expectation values

Rigged Hilbert Space Treatment of Continuous Spectrum

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