Physics – Nuclear Physics – Nuclear Theory
Scientific paper
1995-05-21
Theor.Math.Phys. 104 (1996) 989-1007; Teor.Mat.Fiz. 104N2 (1995) 281-303
Physics
Nuclear Physics
Nuclear Theory
90 kB, LaTeX, no pictures; Final published version of the paper
Scientific paper
10.1007/BF02065979
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.
No associations
LandOfFree
Removal of the Energy Dependence from the Resolvent-like Energy-Dependent Interactions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Removal of the Energy Dependence from the Resolvent-like Energy-Dependent Interactions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Removal of the Energy Dependence from the Resolvent-like Energy-Dependent Interactions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-288296