Using Special Rules for Transformation of the Finding Exact Solutions of the Singular Schrödinger Differential Equation
Abstract
In this article we give a very brief outline of one way of carrying out the spectral analysis of a boundary value problem with specified singularities and investigating the corresponding inverse problem. We find out the solutions of equation satisfying the boundary condition
y¢(0) - aly(0) = 0
where V is a real valued function, λ is a spectral parameter and a is a natural number. As the mention above, these solutions of a singular boundary value problem were made of our premises which
results came out the solutions of a non singular boundary value problem
¢¢ - ( ) + 2 = 0, Î = [0,¥), y V x y l y x R+
y¢(0) - aly(0) = 0.
References
- Agranovich, Z.S., Marchenko, V.A., 1963.The Inverse Problem of Scattering Theory, Science Publishers New York and London. 9. 147-153.
- Bairamov, E., Çakar, Ö., Çelebi, A.O., 1997. Quadratic pencil of Schrödinger operators with spectral singularities: Discrete spectrum and principal functions, J.Math. Anal. Appl. 216 , 303-320.
- Bairamov, E., Çakar, Ö., Krall, A.M., 1999. Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition, J. Differential Equations, 151, 252-267.
- Bairamov, E., Çakar, Ö., Krall, A.M., 1999.An eigenfunction expansion for a quadratic pencil of a Schrödinger operator with spectral singularities, J. Differential Equations, 151, 268-289.
- Bairamov, E., Çelebi, A.O., 1997. Spectral properties of the Klein-Gordon s-wave equation with complex potential, Indian J. Pure Appl. Math., 28 (6), 813-824..
- Naimark, M.A.,1968. Linear Differential Operators II, Ungar, New York. P.260-265.
- Karaman, Ö., Yanık, C., 2000. On the Solutions of Klein- Gordon Equation, Comm. Fac. Sci. Univ., Ank., Vol 49, 139-144.
Singülerliğe Sahip Schrödinger Diferansiyel Denkleminin Çözümlerinin Özel Bir Dönüsüm Yardımı ile Bulunması
Abstract
Bu makalede özel bir singüleriteye sahip sınır değer probleminin, spektral analizinin
incelenmesinde kısa bir yöntemi verilecektir.
singüler diferansiyel denkleminin
y¢(0) - aly(0) = 0
sınır kosulunu gerçekleyen çözümlerini
¢¢ - ( ) + 2 = 0, Î = [0,¥), y V x y l y x R+
y¢(0) - aly(0) = 0
singüler olmayan diferansiyel denkleminin sınır değer problemini gerçekleyen çözümleri yardımı ile
bulunduğu gösterilecektir. Burada V kompleks değerli bir fonksiyon, a bir doğal sayı ve λ bir
parametredir.
References
- Agranovich, Z.S., Marchenko, V.A., 1963.The Inverse Problem of Scattering Theory, Science Publishers New York and London. 9. 147-153.
- Bairamov, E., Çakar, Ö., Çelebi, A.O., 1997. Quadratic pencil of Schrödinger operators with spectral singularities: Discrete spectrum and principal functions, J.Math. Anal. Appl. 216 , 303-320.
- Bairamov, E., Çakar, Ö., Krall, A.M., 1999. Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition, J. Differential Equations, 151, 252-267.
- Bairamov, E., Çakar, Ö., Krall, A.M., 1999.An eigenfunction expansion for a quadratic pencil of a Schrödinger operator with spectral singularities, J. Differential Equations, 151, 268-289.
- Bairamov, E., Çelebi, A.O., 1997. Spectral properties of the Klein-Gordon s-wave equation with complex potential, Indian J. Pure Appl. Math., 28 (6), 813-824..
- Naimark, M.A.,1968. Linear Differential Operators II, Ungar, New York. P.260-265.
- Karaman, Ö., Yanık, C., 2000. On the Solutions of Klein- Gordon Equation, Comm. Fac. Sci. Univ., Ank., Vol 49, 139-144.
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | June 30, 2008 |
| Acceptance Date | January 3, 2008 |
| Published in Issue | Year 2008 Volume: 11 Issue: 1 |