On the Eigenvalues of the Bounded Harmonic Oscillator

Valter Franceschini; Sandro Graffi; Sergio Levoni

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1975)

  • Volume: 58, Issue: 2, page 205-214
  • ISSN: 0392-7881

How to cite

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Franceschini, Valter, Graffi, Sandro, and Levoni, Sergio. "On the Eigenvalues of the Bounded Harmonic Oscillator." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 58.2 (1975): 205-214. <http://eudml.org/doc/291305>.

@article{Franceschini1975,
author = {Franceschini, Valter, Graffi, Sandro, Levoni, Sergio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {eng},
month = {2},
number = {2},
pages = {205-214},
publisher = {Accademia Nazionale dei Lincei},
title = {On the Eigenvalues of the Bounded Harmonic Oscillator},
url = {http://eudml.org/doc/291305},
volume = {58},
year = {1975},
}

TY - JOUR
AU - Franceschini, Valter
AU - Graffi, Sandro
AU - Levoni, Sergio
TI - On the Eigenvalues of the Bounded Harmonic Oscillator
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1975/2//
PB - Accademia Nazionale dei Lincei
VL - 58
IS - 2
SP - 205
EP - 214
LA - eng
UR - http://eudml.org/doc/291305
ER -

References

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  1. CHANDRASEKHAR, S. (1943) - Dynamical Friction, II, «Astr. Jour.», 263-273. Zbl0060.46306MR8000DOI10.1086/144487
  2. AULUCK, F. C. and KOTHARI, D. S. (1945) - The Quantum mechanics of a bounded linear harmonic oscillator, «Proc. Cambridge Phyl. Soc.», 41, 175-179. MR12349DOI10.1017/s0305004100022520
  3. BAIJAL, J. S. and SINGH, K. K. (1955) - The energy levels and the transition probabilities for a bounded linear harmonic oscillator, «Progr. Theor. Phys.», 14, 214-224. Zbl0065.43201MR78913DOI10.1143/PTP.14.214
  4. DEAN, P. (1966) - The constrained quantum mechanical harmonic oscillator, «Proc. Cambridge Phyl. Soc.», 62, 277-286. MR191295DOI10.1017/s0305004100039840
  5. VAWTER, R. (1968) - Effects of finite boundaries on a one-dimensional harmonic oscillator, «Phys. Rev.», 174, 749-757. 
  6. VAWTER, R. (1973) - Energy eigenvalues of a bounded centrally located harmonic oscillator, «Jour. Math. Phys.», 14, 1864-1870. 
  7. FICHERA, G. (1965) - Linear elliptic differential systems and eigenvalue Problem, «Lecture Notes in Math.», 8, Springer-Verlag, Berlin-Heidelberg-New York. Zbl0138.36104MR209639
  8. FICHERA, G. (1973) - Abstract and numerical aspects of eigenvalue theory, «Dep. Math.», Un. of Alberta, Echmonton, Alberta, Canada. 
  9. FICHERA, G. (1974) - Metodi e risultati concernenti l'analisi numerica e qualitativa, «Mem. Acc. Naz. dei Lincei», ser. VIII, 12 (1). Zbl0334.65002MR639162
  10. See, e.g., the treatment of Ref.[7], [8], [9] above. 
  11. MIKHLIN, S. G. and SMOLITSKIY, K. L. (1967) - Approximate solutions of differential and integral equations, Elsevier, New York, London, Amsterdam, Chapt. 3, §2, 8. MR218019

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