Re: 每天收获记录于此

Try to use english,

today I read this paper,,,

Morlet wavelets in quantum mechanics

Authors: John Ashmead

(Submitted on 1 Jan 2010)

Abstract: Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the use of plane wave or delta function decomposition. Morlet wavelets are particularly well-suited for this work: as Gaussians, they have a simple analytic form and they work well with Feynman path integrals. To take full advantage of Morlet wavelets we need an explicit form for the inverse Morlet transform and a manifestly covariant form for the four-dimensional Morlet wavelet. We supply both here.

the main advantages are

 1. Avoid any need to invoke the notorious "collapse of the wave function" in the analysis of the Stern-Gerlach experiment,

2. Avoid the use of artificial convergence factors or Wick rotation in computing path integrals,

3. Compute path integrals in a time symmetric way.

but I still don't quite understand how this works...

this author also has a long article, maybe useful...

Quantum Time

Authors: John Ashmead

(Submitted on 5 May 2010)

Abstract: Normally we quantize along the space dimensions but treat time classically. But from relativity we expect a high level of symmetry between time and space. What happens if we quantize time using the same rules we use to quantize space? To do this, we generalize the paths in the Feynman path integral to include paths that vary in time as well as in space. We use Morlet wavelet decomposition to ensure convergence and normalization of the path integrals. We derive the Schr\"odinger equation in four dimensions from the short time limit of the path integral expression. We verify that we recover standard quantum theory in the non-relativistic, semi-classical, and long time limits. Quantum time is an experiment factory: most foundational experiments in quantum mechanics can be modified in a way that makes them tests of quantum time. We look at single and double slits in time, scattering by time-varying electric and magnetic fields, and the Aharonov-Bohm effect in time.

Comments:	110 pages, 17 figures, presented shorter form of this as poster at Third International Conference on the Nature and Ontology of Spacetime (Montreal, 2008) and as a talk at the 4th Feynman Festival (Olomouc, 2009).
Subjects:	Quantum Physics (quant-ph)
Cite as:	arXiv:1005.0789v1 [quant-ph]

the Stern-Gerlach experiment is very interesting and worth future study...

10. arXiv:0812.1677 [pdf, ps, other]

Title: On the existence of the "classical trajectories" of atoms in the Stern-Gerlach experiment

Authors: M. Dugic, M. Arsenijevic, J. Jeknic-Dugic

Comments: Latex, 13 pages, no figures

Subjects: Quantum Physics (quant-ph)

. arXiv:quant-ph/0511276 [pdf, ps, other]

Title: A complete analysis of the Stern-Gerlach experiment using Pauli spinors

Authors: Michel Gondran, Alexandre Gondran

Comments: 13 pages, 4 figures

Subjects: Quantum Physics (quant-ph)