Point Transformations in Quantum Mechanics. II. Solving for the Generators

Gideon Carmi

doi:10.1103/PhysRevD.7.1044

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Point Transformations in Quantum Mechanics. II. Solving for the Generators

Gideon Carmi

Department of Physics, St. John's University, Jamaica, New York 11432

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Phys. Rev. D 7, 1044 – Published 15 February, 1973

DOI: https://doi.org/10.1103/PhysRevD.7.1044

Abstract

We generalize the method and the results of paper I (G. Carmi, preceding paper) to find the generators of a point transformation which maps the $x_{i}$ , $i = 1, \dots, n$ , into any set of functions $ω_{i} (x_{1}, \dots, x_{n})$ , $i = 1, \dots, n$ , within a certain, quite wide family, for which these generators can be written in closed form, with the object of applications to a quantum many-body method developed by Gross et al.

References (14)

E. P. Gross, in Physics of Many-Particle Systems, edited by E. Meeron (Gordon and Breach, New York, 1966), Vol. 1, pp. 231-406 F. M. Eger and E. P. Gross, J. Math. Phys. 7, 578 (1966) E. P. Gross, Ann. Phys. (N.Y.) 52, 383 (1969)
([3])
G. Carmi, preceding paper, Phys. Rev. D 7, 1038 (1973)
Professor Donald Newman, private communication
Omitted endnote
[D. Bohm and D. Pines, Phys. Rev. 92, 609 (1953)] [G. Carmi and A. J. Lock, Phys. Rev. A 5, 1447 (1972)] [1] [1]
Omitted endnote
Omitted endnote
Omitted endnote
Robert Hermann, Lie Groups and Physics (Benjamin, New York, 1966), p. 139
L. Van Hove, Acad. Roy. Belg. Cl. Sci. Mém. (Series 8) 26, No. 6 (1951) Bull. Cl. Sci. Acad. Roy. Belg. (Series A) 37, 610 (1951)
Omitted endnote
Omitted endnote
Omitted endnote

[c1] E. P. Gross, in Physics of Many-Particle Systems, edited by E. Meeron (Gordon and Breach, New York, 1966), Vol. 1, pp. 231-406 F. M. Eger and E. P. Gross, J. Math. Phys. 7, 578 (1966) E. P. Gross, Ann. Phys. (N.Y.) 52, 383 (1969)

[c2] ([3])

[c3] G. Carmi, preceding paper, Phys. Rev. D 7, 1038 (1973)

[c4] Professor Donald Newman, private communication

[c5] Omitted endnote

[c6] [D. Bohm and D. Pines, Phys. Rev. 92, 609 (1953)] [G. Carmi and A. J. Lock, Phys. Rev. A 5, 1447 (1972)] [1] [1]

[c7] Omitted endnote

[c8] Omitted endnote

[c9] Omitted endnote

[c10] Robert Hermann, Lie Groups and Physics (Benjamin, New York, 1966), p. 139

[c11] L. Van Hove, Acad. Roy. Belg. Cl. Sci. Mém. (Series 8) 26, No. 6 (1951) Bull. Cl. Sci. Acad. Roy. Belg. (Series A) 37, 610 (1951)

[c12] Omitted endnote

[c13] Omitted endnote

[c14] Omitted endnote

Physical Review D

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Point Transformations in Quantum Mechanics. II. Solving for the Generators

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References (14)

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