Sturmian basis functions for the harmonic oscillator

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 62, Issue 2, 2000, Pages 022104-022101

  Szmytkowski, Radosław ^a   Zywicka Mozejko, Bozena ^a  

^a GDANSK UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; HARMONIC ANALYSIS; ONE DIMENSIONAL; POLYNOMIALS;

HARMONIC OSCILLATOR; HERMITE POLYNOMIAL; STURMIAN BASIS FUNCTION; WHITTAKER EQUATION;

QUANTUM THEORY;

EID: 0034246511     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. M. Rotenberg, Adv. At. Mol. Phys. 6, 233 (1970).
2. E. J. Weniger, J. Math. Phys. 26, 276 (1985).
3. N. L. Manakov, V. D. Ovsiannikov, and L. P. Rapoport, Phys. Rep. 141, 319 (1986).
4. E. Karule and R. H. Pratt, J. Phys. B 24, 1585 (1991).
5. N. L. Manakov, A. Maquet, S. I. Marmo, and C. Szymanowski, Phys. Lett. A 237, 234 (1998).
6. A. Maquet, V. Véniard, and T. A. Marian, J. Phys. B 31, 3743 (1998).
7. F. Antonsen, Phys. Rev. A 60, 812 (1999).
8. R. Szmytkowski, J. Phys. B 30, 825 (1997); 30, 2747(E) (1997).
9. R. Szmytkowski, J. Phys. B 30, 825 (1997); 30, 2747(E) (1997).
10. R. Szmytkowski, J. Phys. A 31, 4963 (1998); 31, 7415(E) (1998).
11. R. Szmytkowski, J. Phys. A 31, 4963 (1998); 31, 7415(E) (1998).
12. R. Szmytkowski, e-print physics/9902050.
13. R. Szmytkowski, J. Phys. A 33, 427 (2000).
14. E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations Pis. I & II (Oxford University Press, Oxford, 1958-1962).
15. B. M. Levitan and I. S. Sargsjan, Introduction to Spectral Theory: Selfadjoint Ordinary Differential Operators (American Mathematical Society, Providence, RI, 1975).
16. B. M. Levitan and I. S. Sargsjan, Sturm-Liouville and Dirac Operators (Nauka, Moscow, 1988) (in Russian).
17. The validity of the relations (46) and (57) follows from general theorems of functional analysis [12-14] but may be also proved directly in the way analogous to that in which N. Mukunda [Am. J. Phys. 46, 910 (1978)] proved the completeness of the radial Coulomb wave functions.
18. W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd ed. (Springer, Berlin, 1966).
19. H. Buchholz, The Confluent Hypergeometric Function (Springer, Berlin, 1969).