TY - JOUR
T1 - Quasilinearization method and summation of the WKB series
AU - Krivec, R.
AU - Mandelzweig, V. B.
PY - 2005/4/11
Y1 - 2005/4/11
N2 - Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. Expansion of the pth QLM iterate in powers of h reproduces the structure of the WKB series generating an infinite number of the WKB terms with the first 2p terms reproduced exactly. The QLM quantization condition leads to exact energies for the Pöschl-Teller, Hulthén, Hylleraas, Morse, Eckart potentials, etc. For other, more complicated potentials the first QLM iterate, given by the closed analytic expression, is extremely accurate. The iterates converge very fast. The sixth iterate of the energy for the anharmonic oscillator and for the two-body Coulomb-Dirac equation has an accuracy of 20 significant figures.
AB - Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. Expansion of the pth QLM iterate in powers of h reproduces the structure of the WKB series generating an infinite number of the WKB terms with the first 2p terms reproduced exactly. The QLM quantization condition leads to exact energies for the Pöschl-Teller, Hulthén, Hylleraas, Morse, Eckart potentials, etc. For other, more complicated potentials the first QLM iterate, given by the closed analytic expression, is extremely accurate. The iterates converge very fast. The sixth iterate of the energy for the anharmonic oscillator and for the two-body Coulomb-Dirac equation has an accuracy of 20 significant figures.
KW - Nonlinear differential equations
KW - Quasilinearization
KW - WKB
UR - http://www.scopus.com/inward/record.url?scp=15244361179&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2005.01.072
DO - 10.1016/j.physleta.2005.01.072
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AN - SCOPUS:15244361179
SN - 0375-9601
VL - 337
SP - 354
EP - 359
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 4-6
ER -