| Title:
|
Schrödinger eigenvalue problem for the Gaussian potential (English) |
| Author:
|
Trlifaj, Ladislav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
22 |
| Issue:
|
3 |
| Year:
|
1977 |
| Pages:
|
189-198 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The radial Schrödinger equation with an attractive Gaussian potential and a general angular momentum is transformed by means of the modified Laplace transformation into a linear homogeneous differential equation of the first order with one "retarded" argument. Owing to the fusion of the arguments at the point $z=0$ its integration is possible by an iteration procedure. The discrete spectrum differs from the continuous one by the boundary condition at $z=\infty$ which determines the explicit equation for the energy eigenvalues. The properties of the resolvent are investigated in detail on the real half-axis and various approximations are dicussed. () |
| MSC:
|
34L99 |
| MSC:
|
35J10 |
| idZBL:
|
Zbl 0372.34016 |
| idMR:
|
MR0447783 |
| DOI:
|
10.21136/AM.1977.103692 |
| . |
| Date available:
|
2008-05-20T18:07:08Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103692 |
| . |
| Reference:
|
[1] А. О. Гельфонд: Исчисление конечных разностей.Гос. изд. Физ.-Мат. Лит., Москва, 1959. Zbl 1047.90504 |
| Reference:
|
[2] А. О. Myschkis: Lineare Differentialgleichungen mit nacheilendem Argument.Deutscher Verlag der Wissenschaften, Berlin, 1955. Zbl 0067.31802, MR 0073844 |
| Reference:
|
[3] E. Pinney: Ordinary Difference-Differential Equations.University of California Press, Berkeley and Los Angeles, 1958. Zbl 0091.07901, MR 0097597 |
| Reference:
|
[4] К. Г. Валеев И. Р. Карганьян: .в сборнике: Функциональные и дифференциально-разностные уравнения. Издание Института математики АН УССР, Киев, 1974. Zbl 1235.49003 |
| Reference:
|
[5] S. Flügge: Practical Quantum Mechanics I.Springer-Verlag, Berlin-Heidelberg-New York, 1971. MR 1746199 |
| Reference:
|
[6] B. van der Pol H. Bremer: Operational Calculus Based on the Two-sided Laplace Integral.Cambridge, 1950. MR 0038476 |
| Reference:
|
[7] G. Doetsch: Handbuch der Laplace-Transformation vol. I + II.Birkhäuser Verlag, Basel and Stuttgart, 1950+ 1955. MR 0344808 |
| Reference:
|
[8] H. Bateman: Higher Transcendental Functions vol. III.McGraw-Hill Book Com., New York, Toronto and London, 1955. Zbl 0064.06302, MR 0066496 |
| Reference:
|
[9] A. de Shalit I. Talmi: Nuclear Shell Theory.Academic Press, New York and London, 1963. MR 0154642 |
| . |
