A new look at the quantum mechanics of the harmonic oscillator

Annalen der Physik (Leipzig)

Volumn 16, Issue 7-8, 2007, Pages 439-528

  Kastrup, H A ^a  

^a DESY   (Germany)

Author keywords

Angle and action variables; Harmonic oscillator; Quantum mechanics; Quantum optics

Indexed keywords

ALGEBRA; ELECTRIC FIELDS; OSCILLATORS (ELECTRONIC); QUANTUM OPTICS;

ACTION VARIABLES; HARMONIC OSCILLATOR; LIE ALGEBRA; POISSON BRACKETS;

QUANTUM THEORY;

EID: 34547673150     PISSN: 00033804     EISSN: 15213889     Source Type: Journal    
DOI: 10.1002/andp.200610245     Document Type: Article

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264. E. Hille, Analytic Function Theory II, 2nd edition (Chelsea Publ. Co., New York, 1987), Chap. 14;
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270. M. A. Evgrafov, Asymptotic Estimates and Entire Functions, Russian Tracts on Advanced Mathematics and Phys. IV (Gordon and Breach, Science Publ., Inc., New York, 1961), Chap.III, here pp. 149-151;
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275. [46], formula 3.613 2.
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285. [1l1] V. Bargmann, first of the papers [82], pp. 203-204.
286. [79], Chap. X. 12.
287. [26], Chap. V, sees. D-F; in eq. (103) there one has 2t = u.
288. E.C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd edition (Oxford Univ. Press, London etc., 1950), Sect. 3.16;
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297. N. A. Kawakami, M. C Nemes, and W. F. Wreszinski, e-print arXiv:math-ph/0611025.
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299. W.H. Louisell, Quantum Statistical Properties of Radiation (John Wiley & Sons, New York etc., 1973), Sect. 4.3;
300. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge etc., 1995), Sect. 10.2;
301. WP. Schleich, [36], Sects. 10.2 and 10.3.
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308. Vol. 12, p. 285;
309. Vol. 14, p. 341 (VCH Publ., Inc., New York etc., 1994-96).
310. G. Cantatore (PVLAS Collaboration), Talk given at the Workshop "Axions at the Institute for Advanced Study, Oct. 20-23, 2006"; slides available under http://www.sns.ias.edu/~axions/schedule.shtml.
311. 2 in Space, Paris, Sept. 1999, Cambridge Contemporary Astrophysics Series (Cambridge Univ. Press, Cambridge, 2001);
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313. L. Landau, Z. Phys. 64, 629 (1930);
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315. W Thirring, Quantum Mathematical Phys., 2nd edition, corr. and rev. 2nd printing (Springer-Verlag, Heidelberg etc., 2003), pp. 109-110; 410-412. [126] [46], p. 89, formula 2.282 2.
316. [46], p.81, formula 2.261.
317. [46], p. 89, formula 2.281.
318. V. Bargmann, Ann. Math. 48, 568 (1947).
319. [104], p.79, formula (4).
320. [104], p. 79, formula (9).
321. [104], p. 80, formulae (10) and (11) for n = 0.
322. [104], p. 79, formula (1).
323. J. Spanier and K. B. Oldham, An Atlas of Functions (Hemisphere Publ. Corpor. - Taylor & Francis Group -, NewYork etc., 1987), Fig. 50-1 on p. 490.