Zero-curvature solutions of the one-dimensional Schrödinger equation

Physica Scripta

Volumn 72, Issue 2-3, 2005, Pages 122-126

  Belloni, M ^a   Doncheski, M A ^b   Robinett, R W ^c  

^a DAVIDSON COLLEGE   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

^c PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; EIGENVALUES AND EIGENFUNCTIONS; ELECTRON ENERGY LEVELS; FUNCTIONS; HAMILTONIANS; INTEGRAL EQUATIONS; KINETIC ENERGY; MATHEMATICAL MODELS; SEMICONDUCTOR QUANTUM WELLS; WAVE EQUATIONS;

ANGULAR MOMENTUM STATES; DIRAC DELTA FUNCTION; ZERO-CURVATURE SOLUTIONS; ZERO-ENERGY WAVEFUNCTIONS;

QUANTUM THEORY;

EID: 23344446202     PISSN: 00318949     EISSN: None     Source Type: Journal    
DOI: 10.1238/Physica.Regular.072a00122     Document Type: Review

References (27)

1. Nesvizhevsky, V. V. et al. Nature 415, 297 (2002);
2. Phys. Rev. D 67, 102002 (2003);
3. Phys. Rev. D 68, 108702 (2003).
4. Meekhof, D. M., Monroe, C., King, B. E., Itano, W. M. and Wineland, D. J., Phys. Rev. Lett. 76, 1796 (1996).
5. Bonvalel. A. et al., Phys. Rev. Lett. 76, 4392 (1996).
6. Venugopalan, V. and Agarwal, G. S., Phys. Rev. A 59, 1413(1999);
7. Aronstein, D. L. and Stroud, C. R. Jr., Phys. Rev. A 62, 022102 (2000);
8. Am. J. Phys. 68, 943 (2000).
9. Vugalter, G. A., Das, A. K. and Sorokin, V. A., Phys. Rev. A 66, 012104 (2002).
10. de la Torre, A. C., Mártin, H. O. and Goyeneche, D., Phys. Rev. E 68, 031103 (2003).
11. Schmidt, A. G. M., Cheng, B. K. and da Luz, M. G. E., Phys. Rev. A 66, 062712 (2002).
12. Schmidt. A. G. M. and da Luz, M. G. E., Phys. Rev. A 69, 052708 (2004).
13. Segre, C. U. and Sullivan, J. D., Am. J. Phys. 44, 729 (1976). This paper was one of the first to describe wave packet revivals, as well as to consider the effect of Δ-function barriers on such behavior in the context of the infinite square well.
14. Kuhl, U. and Stöckman, H. J., Physics E (Amsterdam) 9, 384 (2001);
15. Kuhl, U., Izrailev, F. M., Krokhin, A. A. and Stöckman, H. J., Appl. Phys. Lett. 77, 633 (2000);
16. Kühl, U. and Stockman, H. J., Phys. Rev. Lett. 80, 3232 (1998).
17. While these bound-state ZC solutions in 1D are not often discussed, a linear radial wave function, u(r), naturally occurs in low-energy S-wave scattering from finite potentials [12] which are often used as a model for low-energy nuclear scattering [13].
18. Sakurai, J. J., "Modern quantum mechanics", Revised Edition (Addison-Wesley, New York, 1994) Section 7.7.
19. Blatt, J. M. and Weisskopf, V. F., "Theoretical nuclear physics" (John Wiley and Sons, New York, 1952) Sections 2.2-2.3.
20. One can, of course, solve for the quantized energy eigenvalues and normalized wavefunctions for general E > 0 and E < 0 solutions with the additional δ-function interaction, and both yield the results here in the limit that E→0.
21. Sprung, D. W. L., Wu, H. and Martorell, J., Am. J. Phys. 64, 136 (1996).
22. Cooper, F., Khare, A. and Sukhatme, U., Phys. Rep. 251, 267 (1995);
23. "Supersymmetry in quantum mechanics" (Singapore: World Scientific Press, 2002)
24. Aretéva, J. et al. (Guest Editors) J. Phys. A: Math. Gen 37 (2004), Special issue dedicated to the subject of the "International Conference on progress in supersymmetric quantum mechanics) (PSQM'03).
25. Dunne, G. and Feinberg, J., Phys. Rev. D 57, 1271 (1998);
26. Khare, A. and Sukhatme, U., J. Phys. A: Math. Gen. 37, 10037 (2004).
27. Gilbert, L. P., Belloni, M., Doncheski, M. A. and Robinett, R. W., to be submitted for publication.