172 research outputs found
The Feynman Path Integral: An Historical Slice
Efforts to give an improved mathematical meaning to Feynman's path integral
formulation of quantum mechanics started soon after its introduction and
continue to this day. In the present paper, one common thread of development is
followed over many years, with contributions made by various authors. The
present version of this line of development involves a continuous-time
regularization for a general phase space path integral and provides, in the
author's opinion at least, perhaps the optimal formulation of the path
integral.Comment: LaTeX, 24 pages, no figure
Coherent States for the Hydrogen Atom
The long-standing problem of finding coherent states for the (bound state
portion of the) hydrogen atom is positively resolved. The states in question:
(i) are normalized and are parameterized continuously, (ii) admit a resolution
of unity with a positive measure, and (iii) enjoy the property that the
temporal evolution of any coherent state by the hydrogen atom Hamiltonian
remains a coherent state for all time.Comment: 8 pages, TeX, no figure
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