We prove a 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.
Nous démontrons un théorème de déformation verselle analytique pour l’algèbre de Heisenberg dans le cas . Nous définissons le spectre d’un élément dans cette algèbre. La quantification du lemme de Morse montre que les séries perturbatives du spectre de l’oscillateur harmonique deviennent analytique après une transformation de Borel formelle.
Keywords: Harmonic oscillator, Borel summability, micro-local analysis, non-commutative geometry
Mot clés : oscillateur harmonique, sommabilité de Borel, analyse semi-classique, formes normales
@article{AIF_2009__59_5_2061_0, author = {Garay, Mauricio D.}, title = {Perturbative expansions in quantum mechanics}, journal = {Annales de l'Institut Fourier}, pages = {2061--2101}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {59}, number = {5}, year = {2009}, doi = {10.5802/aif.2483}, mrnumber = {2573197}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2483/} }
TY - JOUR AU - Garay, Mauricio D. TI - Perturbative expansions in quantum mechanics JO - Annales de l'Institut Fourier PY - 2009 SP - 2061 EP - 2101 VL - 59 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2483/ DO - 10.5802/aif.2483 LA - en ID - AIF_2009__59_5_2061_0 ER -
%0 Journal Article %A Garay, Mauricio D. %T Perturbative expansions in quantum mechanics %J Annales de l'Institut Fourier %D 2009 %P 2061-2101 %V 59 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2483/ %R 10.5802/aif.2483 %G en %F AIF_2009__59_5_2061_0
Garay, Mauricio D. Perturbative expansions in quantum mechanics. Annales de l'Institut Fourier, Volume 59 (2009) no. 5, pp. 2061-2101. doi : 10.5802/aif.2483. http://archive.numdam.org/articles/10.5802/aif.2483/
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