On the nondegeneracy theorem for a particle in a box

Brazilian Journal of Physics

Volumn 38, Issue 3 A, 2008, Pages 355-361

  De Vincenzo, Salvatore ^a  

^a FACULTAD DE CIENCIAS   (Venezuela)

Author keywords

Invariance; Nondegeneracy theorem; Particle in a box; Quantum mechanics; Time reversal

Indexed keywords

EID: 52949107631     PISSN: 01039733     EISSN: None     Source Type: Journal    
DOI: 10.1590/S0103-97332008000300009     Document Type: Article

References (31)

1. R. Loudon, Am. J. Phys. 27, 649 (1959).
2. A. N. Gordeyev and S. C. Chhajlany, J. Phys. A: Math. Gen. 30, 6893 (1997).
3. J. M. Cohen and B. Kuharetz, J. Math. Phys. 34, 12 (1993).
4. U. Oseguera, Eur. J. Phys. 11, 35 (1990).
5. J. Goldstein, C. Lebiedzik, and R. W. Robinett, Am. J. Phys. 62, 612 (1994).
6. J. W. Dettman, Mathematical Methods in Physics and Engineering (Dover, New York, 1988), pp 182-3.
7. R. Shankar Principles of quantum mechanics 2nd edn., (Plenum., New York, 1994), p 176.
8. D. J. Griffiths Introduction to Quantum Mechanics (Prentice-Hall, Upper Saddle River, NJ, 1995), p 69.
9. L. D. Landau and E. M. Lifshitz Quantum Mechanics - Non- relativistic Theory 3rd edn., (Butterworth-Heinemann, New Delhi, 2000), p 60.
10. K. Bhattacharyya and R. K. Pathak, Int. J. Quantum. Chem. 59, 219 (1996).
11. S. Kar and R. R. Parwani, Can degenerate bound states occur in one dimensional quantum mechanics? Preprint quant-ph/0706.1135v1 (2007).
12. V. Alonso and S. De Vincenzo, J. Phys. A: Math. Gen. 30, 8573 (1997).
13. T. Fülöp and I. Tsutsui, Phys. Lett. A 264, 366 (2000).
14. Z. Brzeźniak and B. Jefferies, J. Phys. A: Math. Gen. 34, 2977 (2001).
15. G. Bonneau, J. Faraut, and G. Valent, Am. J. Phys. 69, 322 (2001).
16. G. Bonneau, J. Faraut and G. Valent, Self-adjoint extensions of operators and the teaching of quantum mechanics, Preprint quant-ph/0103153 (2001). This is an extended version, with mathematical details.
17. C. Filgueiras and F. Moraes, Extensões auto-adjuntas de operadores em mecânica quântica (in Portuguese), Rev. Bras. Ens. de Fis. 29, 11 (2007).
18. M. Carreau, E. Farhi, and S. Gutmann, Phys. Rev. D 42, 1194 (1990).
19. V. Alonso, S. De Vincenzo, and L. González-Díaz, Phys. Lett. A 287, 23 (2001).
20. S. Albeverio and P. Kurasov Singular Perturbations of Differential Operators (University Press, Cambridge, 2000), p 145.
21. S. Albeverio, L. Dabrowski, and P. Kurasov, Lett. Math. Phys. 45, 33 (1998).
22. F A. B. Coutinho, Y. Nogami, and J. Fernando Perez, J. Phys. A: Math. Gen. 32, L133 (1999).
23. W. A. Atkinson and M. Razavy, Can. J. Phys. 71, 380 (1993).
24. V. S. Araujo, F. A. B. Coutinho, and F. M. Toyama, Braz. J. Phys. 38, 178 (2008).
25. C. Yuce, Non-hermitian Hamiltonians with real spectra in quantum mechanics, Preprint quant-ph/0702205 v2 (2007).
26. K. E. Gustafson Introduction to Partial Differential Equations and Hilbert Space Methods 3rd edn., (Dover, New York, 1999), p 175.
27. G. B. Arfken and H. J. Weber Mathematical Methods for Physicists (Academic Press, Burlington, MA, 2001), p 575.
28. J. M. Cohen and B. Kuharetz, J. Math. Phys. 34, 4964 (1993).
29. M. Moriconi, Am. J. Phys. 75, 284 (2007).
30. A. Z. Capri, Am. J. Phys. 45, 823 (1977).
31. S. De Vincenzo, Some results for a particle in a box and their supersymmetric partners (2007). Submitted to publication.