Showing papers on "Quantum geometry published in 1971"
TL;DR: In this paper, the operator solutions of the Schwinger model are given in several gauges and the correct interpretation for the covariant solution with indefinite metric is discussed, and a class of noncovariant gauges, particularly well suited to the analysis of the gauge-invariant algebra is obtained.
480 citations
TL;DR: The classical motion of a particle on a surface is simulated in quantum mechanics by forcing the particle to move between two parallel surfaces with distance d. In the limit d → 0 one obtains an equation which differs from the equation proposed originally by Schrodinger by an additional potential depending on the curvature of the surface as discussed by the authors.
320 citations
TL;DR: In this article, a method for extracting from data the quantum theoretical state representation belonging to any reproducible empirical scheme for preparing a physical system, provided only that at least one observable has its possible values limited to a finite set.
Abstract: This paper develops a method for extracting from data the quantum theoretical state representation belonging to any reproducible empirical scheme for preparing a physical system, provided only that at least one observable has its possible values limited to a finite set. In Part I, we formulate a general systematic procedure, based on the concept of irreducible tensor operators, for the selection of sets of observables sufficiently large to permit the unambiguous determination of an unknown quantum state.
61 citations
01 Jan 1971
57 citations
TL;DR: In this paper, it was shown that if the real field admits a certain type of observable (together with other structure which seems to be physically justified), then the real fields contain the real subfield as a subfield.
Abstract: Corresponding to any irreducible proposition system L in general quantum mechanics there is a division ring D with an anti‐automorphism * and a vector space (V, D) over D with a definite sesquilinear form φ such that L is isomorphic to the set of φ closed subspaces of (V, D). The main task remaining in connecting the general quantum mechanics to the conventional quantum theory in a complex Hilbert space is to give physical arguments which force D to be the complex field. In this paper it is shown that if L admits a certain type of observable (together with other structure which seems to be physically justified), then D contains the real field as a subfield. Steps are then indicated that can be taken to move from the reals to the complexes or quaternions.
23 citations
TL;DR: In this paper, the authors considered the infinite square-well potential as a limiting case of an finite squarewell potential in quantum mechanics and investigated its boundary condition, and showed that it is an interesting boundary condition.
Abstract: A well-known problem of an infinite square-well potential in quantum mechanics furnishes an interesting boundary condition. We investigate this in detail by considering the infinite square-well potential as a limiting case of an finite square-well potential.
10 citations
Journal Article•
2 citations
01 Jan 1971
TL;DR: The basic quantum mechanics required will be described with a sequence of postulates and definitions with a few comments interpolated to be useful for the practical analysis of NMR spectra.
Abstract: The basic quantum mechanics required will be described with a sequence of postulates and definitions with a few comments interpolated. The treatment does not claim maximum rigour and elegance but is intended to be useful for the practical analysis of NMR spectra.
1 citations