The Cauchy problem of the one dimensional Schrödinger equation with non-local potentials
For a large class of operators A, not necessarily local, it is proved that the Cauchy problem of the Schrödinger equation: −d2f(z)dz2+Af(z)=s2f(z), f(0)=0, f′(0)=1 possesses a unique solution in the Hilbert (H2(Δ)) and Banach (H1(Δ)) spaces of analytic functions in the unit disc Δ={z:|z|<1}....
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| Format: | Article |
| Language: | English |
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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000985 |
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| _version_ | 1850217616896950272 |
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| author | I. E. Kougias |
| author_facet | I. E. Kougias |
| author_sort | I. E. Kougias |
| collection | DOAJ |
| description | For a large class of operators A, not necessarily local, it is proved that the Cauchy
problem of the Schrödinger equation:
−d2f(z)dz2+Af(z)=s2f(z), f(0)=0, f′(0)=1
possesses a unique solution in the Hilbert (H2(Δ)) and Banach (H1(Δ)) spaces of analytic functions
in the unit disc Δ={z:|z|<1}. |
| format | Article |
| id | doaj-art-37eac53aabce46859732df613b2ba67f |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-37eac53aabce46859732df613b2ba67f2025-08-20T02:08:00ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116479179410.1155/S0161171293000985The Cauchy problem of the one dimensional Schrödinger equation with non-local potentialsI. E. Kougias0Department of Mathematics, University of Patras, Patras, GreeceFor a large class of operators A, not necessarily local, it is proved that the Cauchy problem of the Schrödinger equation: −d2f(z)dz2+Af(z)=s2f(z), f(0)=0, f′(0)=1 possesses a unique solution in the Hilbert (H2(Δ)) and Banach (H1(Δ)) spaces of analytic functions in the unit disc Δ={z:|z|<1}.http://dx.doi.org/10.1155/S0161171293000985Cauchy problemSchrödinger equationHardy-Lebesque spaces. |
| spellingShingle | I. E. Kougias The Cauchy problem of the one dimensional Schrödinger equation with non-local potentials International Journal of Mathematics and Mathematical Sciences Cauchy problem Schrödinger equation Hardy-Lebesque spaces. |
| title | The Cauchy problem of the one dimensional Schrödinger equation with non-local potentials |
| title_full | The Cauchy problem of the one dimensional Schrödinger equation with non-local potentials |
| title_fullStr | The Cauchy problem of the one dimensional Schrödinger equation with non-local potentials |
| title_full_unstemmed | The Cauchy problem of the one dimensional Schrödinger equation with non-local potentials |
| title_short | The Cauchy problem of the one dimensional Schrödinger equation with non-local potentials |
| title_sort | cauchy problem of the one dimensional schrodinger equation with non local potentials |
| topic | Cauchy problem Schrödinger equation Hardy-Lebesque spaces. |
| url | http://dx.doi.org/10.1155/S0161171293000985 |
| work_keys_str_mv | AT iekougias thecauchyproblemoftheonedimensionalschrodingerequationwithnonlocalpotentials AT iekougias cauchyproblemoftheonedimensionalschrodingerequationwithnonlocalpotentials |