A METHOD FOR FINDING POTENTIALS CORRESPONDING TO POLYNOMIAL-FACTOR EIGENFUNCTIONS IN QUANTUM MECHANICS

YANG CEU-LIANG

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2024年10月30日

Chinese Physics C> 1979, Vol. 3> Issue(5) : 541-554

A METHOD FOR FINDING POTENTIALS CORRESPONDING TO POLYNOMIAL-FACTOR EIGENFUNCTIONS IN QUANTUM MECHANICS

YANG CEU-LIANG

Shantung University

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Abstract：
A method for finding potentials corresponding to polynomial-factor eigenfunc-tions is given for the Schr（?）dinger equation as an example.It is shown that theeigen-solutions for harmonic and Columb's potentials in quantum mechanics are the twoexamples which can be given by this method and some other examples are discovered.This method and some results of this paper may be useful for hadron structure mo-del theory.One of the examples is the equation in Ref.（4）which is derived fromBethe-Salpeter equation for the case that the straton is tightly bounded in certain po-tential well.When this method is applied to that equation for three dimensionalcentral symmetric potential V（r）=V₀—2（N+（1/2））β^-1（√V₆r²）+（V₆r⁶）, some resultsare obtained as shown in Fig. 2 in which λ′ must be considered as a linear function of m².The so called“quasic Regge trajectory”behavior is manifested.

References

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R. P. Feynman, Science, 183 (1972), 601.[2] R. F. Keam, Journ. Math, Phys., 10 (1969), 594.[3] M. Bohm et al., Nucl. Phys., 51B (1973), 397;D .Z. Winkel, Journ, Math. Phys, 16 (1975), 93.[4] 胡宁，科学通报，3 (1978), 129:朱重远、安瑛，科学通报，3 (1978) 154.[5] 冼鼎昌等，物理学报，27(1978), 94.[6] A. F. Antippa, A. E. Evertt and A. J. Phares., Nuovo Cimento., 43A (1978), 347.[7] 卡姆克，常微分方程手册，科学出版社，1977.

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YANG CEU-LIANG. A METHOD FOR FINDING POTENTIALS CORRESPONDING TO POLYNOMIAL-FACTOR EIGENFUNCTIONS IN QUANTUM MECHANICS[J]. Chinese Physics C, 1979, 3(5): 541-554.

YANG CEU-LIANG. A METHOD FOR FINDING POTENTIALS CORRESPONDING TO POLYNOMIAL-FACTOR EIGENFUNCTIONS IN QUANTUM MECHANICS[J]. Chinese Physics C, 1979, 3(5): 541-554. shu

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Received: 1978-05-03
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

A METHOD FOR FINDING POTENTIALS CORRESPONDING TO POLYNOMIAL-FACTOR EIGENFUNCTIONS IN QUANTUM MECHANICS

YANG CEU-LIANG

Shantung University

Received Date: 1978-05-03
Accepted Date: 1900-01-01
Available Online: 1979-10-05

Abstract: A method for finding potentials corresponding to polynomial-factor eigenfunc-tions is given for the Schr（?）dinger equation as an example.It is shown that theeigen-solutions for harmonic and Columb's potentials in quantum mechanics are the twoexamples which can be given by this method and some other examples are discovered.This method and some results of this paper may be useful for hadron structure mo-del theory.One of the examples is the equation in Ref.（4）which is derived fromBethe-Salpeter equation for the case that the straton is tightly bounded in certain po-tential well.When this method is applied to that equation for three dimensionalcentral symmetric potential V（r）=V₀—2（N+（1/2））β^-1（√V₆r²）+（V₆r⁶）, some resultsare obtained as shown in Fig. 2 in which λ′ must be considered as a linear function of m².The so called“quasic Regge trajectory”behavior is manifested.