Geodesic
Expansion with respect to~$\hbar$ for bound states of the Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 90 (1992) no. 2, pp. 208-217

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A WKB-complementing $\hbar$ expansion for bound states of the radial Schrödinger equation is discussed. A recursive method for calculating the quantum corrections of any order to the energy of the classical motion is presented. The use of quantization conditions makes it possible to write down recursion relations in an equally simple form for the ground and radially excited states. The connection between the approach and the $1/N$ expansion is considered. It is shown that the method can also be used for analysis in the $(l,E)$ plane in the form of a $\hbar$ expansion for Regge trajectories. 
@article{TMF_1992_90_2_a4,
     author = {S. S. Stepanov and R. S. Tutik},
     title = {Expansion with respect to~$\hbar$ for bound states of the {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {208--217},
     publisher = {mathdoc},
     volume = {90},
     number = {2},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a4/}
}
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S. S. Stepanov; R. S. Tutik. Expansion with respect to~$\hbar$ for bound states of the Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 90 (1992) no. 2, pp. 208-217. http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a4/