INVESTIGATION OF NON-LINFAR SCHRODINGER EQUATION SOLITON SOLUTION

SHI YI-JIN; HE YIN

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2024年10月30日

Chinese Physics C> 1979, Vol. 3> Issue(4) : 418-431

INVESTIGATION OF NON-LINFAR SCHRODINGER EQUATION SOLITON SOLUTION

SHI YI-JIN ,
HE YIN

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Abstract：
Packet-like soliton solution of the non-linear Schrödinger's equation has been in-vestigated.We found that a state of a free particle can possibly be described by thissoliton solution,with the quantum property and the classical property of a particleas its limiting cases.A set of biorthogonal eigen-functions of non-hermitian opera-tor,which can be used in the pertubation expansion,has been found.We discoveredthat the discrete eigenvalue mode corresponds to the“classical”motion of a particle,and the continuous eigenvalue modes correspond to the“quantum”motion.Wesuggested that the parameter u describing the state of a system can be used to identifywhether the system is“quantum”or“classical”.

References

[1]

A. C. Seott. F. Y. F. Chu and D. W. Mclaughlin, Proceedings of the IEEE, 60 (1973), 1443.[2] K. Izumo and K. Konno, Proceedings of the International Conference on Nuclear, Structure, Coutribution Papers, Tokyo (1977), p. 779.[3] L. D. Landay and E. M. Lifshitz in "Quantum Mechanics" Oxford, London: PergamonPress Ltd. 1962, p. 69.[4] M. Morse and Feshbach in "Methods of Theoretical Physics" Vol. 1. N, Y., London,McGrow-Hill Book Company, 1953.

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SHI YI-JIN and HE YIN. INVESTIGATION OF NON-LINFAR SCHRODINGER EQUATION SOLITON SOLUTION[J]. Chinese Physics C, 1979, 3(4): 418-431.

SHI YI-JIN and HE YIN. INVESTIGATION OF NON-LINFAR SCHRODINGER EQUATION SOLITON SOLUTION[J]. Chinese Physics C, 1979, 3(4): 418-431. shu

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Received: 1978-04-17
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

INVESTIGATION OF NON-LINFAR SCHRODINGER EQUATION SOLITON SOLUTION

SHI YI-JIN
HE YIN

Received Date: 1978-04-17
Accepted Date: 1900-01-01
Available Online: 1979-08-05

Abstract: Packet-like soliton solution of the non-linear Schrödinger's equation has been in-vestigated.We found that a state of a free particle can possibly be described by thissoliton solution,with the quantum property and the classical property of a particleas its limiting cases.A set of biorthogonal eigen-functions of non-hermitian opera-tor,which can be used in the pertubation expansion,has been found.We discoveredthat the discrete eigenvalue mode corresponds to the“classical”motion of a particle,and the continuous eigenvalue modes correspond to the“quantum”motion.Wesuggested that the parameter u describing the state of a system can be used to identifywhether the system is“quantum”or“classical”.