High energy asymptotics and trace formulae for the perturbed harmonic oscillator
Pushnitski, Alexander ; Sorrell, Ian
arXiv, 0505131 / Harvested from arXiv
Text on arXiv
A one-dimensional quantum harmonic oscillator perturbed by a smooth compactly supported potential is considered. For the corresponding eigenvalues $\lambda_n$, a complete asymptotic expansion for large $n$ is obtained, and the coefficients of this expansion are expressed in terms of the heat invariants. A sequence of trace formulas is obtained, expressing regularised sums of integer powers of eigenvalues $\lambda_n$ in terms of the heat invariants.
Publié le : 2005-05-08
Classification:  Mathematics - Spectral Theory,  Mathematical Physics,  47E05 (Primary) 34L20 
@article{0505131,
     author = {Pushnitski, Alexander and Sorrell, Ian},
     title = {High energy asymptotics and trace formulae for the perturbed harmonic
  oscillator},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0505131}
}

Pushnitski, Alexander; Sorrell, Ian. High energy asymptotics and trace formulae for the perturbed harmonic
  oscillator. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0505131/