Perturbative expansions in quantum mechanics

Mauricio D. Garay[1]

  • [1] 2A, avenue Édouard Herriot 91440 Bures-sur-Yvette (France)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 5, page 2061-2101
  • ISSN: 0373-0956

Abstract

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We prove a D = 1 analytic versal deformation theorem in the Heisenberg algebra. We define the spectrum of an element in the Heisenberg algebra. The quantised version of the Morse lemma already shows that the perturbation series arising in a perturbed harmonic oscillator become analytic after a formal Borel transform.

How to cite

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Garay, Mauricio D.. "Perturbative expansions in quantum mechanics." Annales de l’institut Fourier 59.5 (2009): 2061-2101. <http://eudml.org/doc/10447>.

@article{Garay2009,
abstract = {We prove a $D=1$ analytic versal deformation theorem in the Heisenberg algebra. We define the spectrum of an element in the Heisenberg algebra. The quantised version of the Morse lemma already shows that the perturbation series arising in a perturbed harmonic oscillator become analytic after a formal Borel transform.},
affiliation = {2A, avenue Édouard Herriot 91440 Bures-sur-Yvette (France)},
author = {Garay, Mauricio D.},
journal = {Annales de l’institut Fourier},
keywords = {Harmonic oscillator; Borel summability; micro-local analysis; non-commutative geometry; harmonic oscillator},
language = {eng},
number = {5},
pages = {2061-2101},
publisher = {Association des Annales de l’institut Fourier},
title = {Perturbative expansions in quantum mechanics},
url = {http://eudml.org/doc/10447},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Garay, Mauricio D.
TI - Perturbative expansions in quantum mechanics
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 5
SP - 2061
EP - 2101
AB - We prove a $D=1$ analytic versal deformation theorem in the Heisenberg algebra. We define the spectrum of an element in the Heisenberg algebra. The quantised version of the Morse lemma already shows that the perturbation series arising in a perturbed harmonic oscillator become analytic after a formal Borel transform.
LA - eng
KW - Harmonic oscillator; Borel summability; micro-local analysis; non-commutative geometry; harmonic oscillator
UR - http://eudml.org/doc/10447
ER -

References

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