×

Algebraic approach to the spectral problem for the Schrödinger equation with power potentials. (English) Zbl 1153.81495

Summary: The method reducing the solution of the Schrödinger equation for several types of power potentials to the solution of the eigenvalue problem for the infinite system of algebraic equations is developed. The finite truncation of this system provides high accuracy results for low-lying levels. The proposed approach is appropriate both for analytic calculations and for numerical computations. This method allows also to determine the spectrum of the Schrödinger-like relativistic equations. The heavy quarkonium (charmonium and bottomonium) mass spectra for the Cornell potential and the sum of the Coulomb and oscillator potentials are calculated. The results are in good agreement with experimental data.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] DOI: 10.1016/0370-1573(79)90095-4 · doi:10.1016/0370-1573(79)90095-4
[2] Mur V. D., Zh. Eksp. Teor. Fiz. 105 pp 3– (1994)
[3] Mur V. D., Zh. Eksp. Teor. Fiz. 104 pp 2293– (1993)
[4] DOI: 10.4213/tmf1215 · doi:10.4213/tmf1215
[5] Vshivtsev A. S., Izvestiya Vuzov. Fiz. 1 pp 95– (1994)
[6] DOI: 10.1016/0370-1573(91)90001-3 · doi:10.1016/0370-1573(91)90001-3
[7] Eichten E., Phys. Rev. 17 pp 3090– (1979)
[8] Particle Data Group (R. M. Barnett et al., ), Phys. Rev. 54 pp 1– (1996)
[9] DOI: 10.1007/BF02750359 · doi:10.1007/BF02750359
[10] Kadyshevsky V. G., At. Yadra 2 pp 637– (1972)
[11] Kang J. S., Phys. Rev. 12 pp 841– (1975)
[12] DOI: 10.1016/0370-1573(78)90151-5 · doi:10.1016/0370-1573(78)90151-5
[13] DOI: 10.1007/BF01017955 · doi:10.1007/BF01017955
[14] Galkin V. O., Yad. Fiz. 55 pp 2175– (1992)
[15] DOI: 10.1002/sapm1969483257 · doi:10.1002/sapm1969483257
[16] DOI: 10.1007/BF01609850 · Zbl 0348.34016 · doi:10.1007/BF01609850
[17] DOI: 10.1016/0370-2693(69)90087-2 · doi:10.1016/0370-2693(69)90087-2
[18] DOI: 10.1016/0771-050X(79)90021-4 · Zbl 0394.65026 · doi:10.1016/0771-050X(79)90021-4
[19] Vshivtsev A. S., Systems 2 pp 23– (1997)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.