General considerations are given to possible extensions of the methods discussed in the book to nonstationary data beyond 1D signals (e.g., multivariate or graph-based). The analogy between signal theory and quantum mechanics formalisms are mentioned, and a general perpsective on further opportunities is outlined as an open conclusion.

Cambridge University Press eBooksAug 22, 20180 citations

Medicinal chemistry

General Considerations of Quantum Theory

Published Jan 1, 1971• 0 citations

Publisher

DOI: 10.1016/b978-0-12-406550-5.50007-0

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We here consider a generalization of the Klein-Gordon scalar wave equation which involves a single arbitrary function. The quantization may be viewed as allowing

\hbar

to be a function of the momentum or wave vector rather than a constant. The generalized theory is most easily viewed in the wave vector space analog of the Lagrangian. We need no reference to spacetime. In the generalized theory the de Broglie relation between wave vector and momentum is generalized, as are the canonical commutation relations and the uncertainty principle. The generalized uncertainty principle obtained is the same as has been derived from string theory, or by a general consideration of gravitational effects during the quantum measurement process. The propagator of the scalar field is also generalized, and an illustrative example is given in which it factors into the usual propagator times a "propagator form factor."