|
Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 104, Number 2, Pages 281–303
(Mi tmf1338)
|
|
|
|
This article is cited in 5 scientific papers (total in 5 papers)
Removal of the dependence on energy from interactions depending on it as a resolvent
A. K. Motovilov Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics
Abstract:
The spectral problem $(A + V(z))\psi =z\psi$ is considered with $A$, a self-adjoint Hamiltonian of sufficiently arbitrary nature. The perturbation $V(z)$ is assumed to depend on the energy $z$ as resolvent of another self-adjoint operator $A':$ $V(z)=-B(A'-z)^{-1}B^{*}$. It is supposed that operator $B$ has a finite Hilbert–Schmidt norm and spectra of operators $A$ and $A'$ are separated. The conditions are formulated when the perturbation $V(z)$ may be replaced with an energy-independent “potential” $W$ such that the Hamiltonian $H=A +W$ has the same spectrum (more exactly a part of spectrum) and the same eigenfunctions as the initial spectral problem. The orthogonality and expansion theorems are proved for eigenfunction systems of the Hamiltonian $ H=A + W$. Scattering theory is developed for $H$ in the case when operator $A$ has continuous spectrum. Applications of the results obtained to few-body problems are discussed.
Received: 06.09.1994
Citation:
A. K. Motovilov, “Removal of the dependence on energy from interactions depending on it as a resolvent”, TMF, 104:2 (1995), 281–303; Theoret. and Math. Phys., 104:2 (1995), 989–1007
Linking options:
https://www.mathnet.ru/eng/tmf1338 https://www.mathnet.ru/eng/tmf/v104/i2/p281
|
Statistics & downloads: |
Abstract page: | 320 | Full-text PDF : | 128 | References: | 67 | First page: | 1 |
|