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Spectral decomposition of the operator p2–q2

✍ Scribed by N.G. Van Kampen

Publisher
Elsevier Science
Year
1958
Weight
543 KB
Volume
24
Category
Article
ISSN
0031-8914

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✦ Synopsis

It is shown that the operator p2 _ q2 has a continuous spectrum extending from --00 to + oo. The expansion of an arbitrary function with respect to the eigenfunctions is given. The action of the operators q and p on the eigenfunctions can be written explicitly by means of symbolic formulae. Finally, an alternative method for studying the behaviour of self-accelerating wave packets is given.

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