Academic Journal
Schrödinger eigenvalue problem for the Gaussian potential
| العنوان: | Schrödinger eigenvalue problem for the Gaussian potential |
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| المؤلفون: | Trlifaj, Ladislav |
| بيانات النشر: | Institute of Mathematics, Academy of Sciences of the Czech Republic Matematický ústav AV ČR |
| سنة النشر: | 1977 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | msc:34L99, msc:35J10 |
| الوصف: | 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. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0373-6725 |
| Relation: | mr:MR0447783; zbl:Zbl 0372.34016; 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 |
| الاتاحة: | http://hdl.handle.net/10338.dmlcz/103692 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.BE74529 |
| قاعدة البيانات: | BASE |
| تدمد: | 03736725 |
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