%0 Journal Article %1 Gaudreau2013261 %A Gaudreau, Philippe %A Slevinsky, Richard M. %A Safouhi, Hassan %D 2013 %J Annals of Physics %K asymptotic eigenvalue equation mathematics mechanics physics quantum schrodinger semiclassical series solution unread %N 0 %P 261 - 277 %R 10.1016/j.aop.2013.07.001 %T An asymptotic expansion for energy eigenvalues of anharmonic oscillators %U http://www.sciencedirect.com/science/article/pii/S0003491613001528 %V 337 %X Abstract In the present contribution, we derive an asymptotic expansion for the energy eigenvalues of anharmonic oscillators for potentials of the form V ( x ) = κ x 2 q + ω x 2 , q = 2 , 3 , … as the energy level n approaches infinity. The asymptotic expansion is obtained using the \WKB\ theory and series reversion. Furthermore, we construct an algorithm for computing the coefficients of the asymptotic expansion for quartic anharmonic oscillators, leading to an efficient and accurate computation of the energy values for n ≥ 6 .

@article{Gaudreau2013261, abstract = {Abstract In the present contribution, we derive an asymptotic expansion for the energy eigenvalues of anharmonic oscillators for potentials of the form V ( x ) = κ x 2 q + ω x 2 , q = 2 , 3 , … as the energy level n approaches infinity. The asymptotic expansion is obtained using the \{WKB\} theory and series reversion. Furthermore, we construct an algorithm for computing the coefficients of the asymptotic expansion for quartic anharmonic oscillators, leading to an efficient and accurate computation of the energy values for n ≥ 6 . }, added-at = {2013-09-04T04:15:02.000+0200}, author = {Gaudreau, Philippe and Slevinsky, Richard M. and Safouhi, Hassan}, biburl = {https://www.bibsonomy.org/bibtex/2c2fb00f6948c16919a440b9e7fdd2db7/drmatusek}, doi = {10.1016/j.aop.2013.07.001}, interhash = {048e69c04b22013277ac3eee73057f75}, intrahash = {c2fb00f6948c16919a440b9e7fdd2db7}, issn = {0003-4916}, journal = {Annals of Physics }, keywords = {asymptotic eigenvalue equation mathematics mechanics physics quantum schrodinger semiclassical series solution unread}, month = oct, number = 0, pages = {261 - 277}, timestamp = {2014-06-29T02:09:57.000+0200}, title = {An asymptotic expansion for energy eigenvalues of anharmonic oscillators }, url = {http://www.sciencedirect.com/science/article/pii/S0003491613001528}, volume = 337, year = 2013 }