56 v 1 2 9 A ug 2 00 5 The inverse problem for perturbed harmonic oscillator on the half - line
نویسنده
چکیده
We consider the perturbed harmonic oscillator TDψ = −ψ′′ + x2ψ + q(x)ψ, ψ(0) = 0 in L(R+), where q ∈ H+ = {q′, xq ∈ L(R+)} is a real-valued potential. We prove that the mapping q 7→ spectral data = {eigenvalues of TD} ⊕ {norming constants} is one-to-one and onto. The complete characterization of the set of spectral data which corresponds to q ∈ H+ is given. Moreover, we solve the similar inverse problem for the family of boundary conditions ψ′(0) = bψ(0), b ∈ R.
منابع مشابه
A ug 2 00 9 CAN CLASSICAL LINEAR HARMONIC OSCILLATOR HOLD CHAOTIC ( FRACTAL ) DYNAMICS
In this work a classical linear harmonic oscillator, evolving during a small time interval (so that simple non-linear, second order Taylor approximation of the dynamics is satisfied) and restarting (by a mechanism) in a strictly chosen series of the time moments, is considered. It is shown that given linear oscillator behaves dynamically analogously to discrete logistic equation, which, as an e...
متن کاملConnectedness of the Isospectral Manifold for One-dimensional Half-line Schrödinger Operators
Let V0 be a real-valued function on [0,∞) and V ∈ L([0, R]) for all R > 0 so that H(V0) = − d 2 dx + V0 in L ([0,∞)) with u(0) = 0 boundary conditions has discrete spectrum bounded from below. Let M(V0) be the set of V so that H(V ) and H(V0) have the same spectrum. We prove that M(V0) is connected. The limitation of our knowledge of inverse spectral theory for Schrödinger operators HR(V ) = − ...
متن کاملSolution of strongly nonlinear oscillator problem arising in Plasma Physics with Newton Harmonic Balance Method
In this paper, Newton Harmonic Balance Method (NHBM) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. Periodic solution is analytically verified and consequently the relation between the Natural Frequency and the amplitude is obtained in an ana...
متن کاملar X iv : m at h / 05 05 46 8 v 2 [ m at h . A P ] 2 2 A ug 2 00 5 INSTABILITY FOR SEMI - CLASSICAL SCHRÖDINGER EQUATIONS
Using WKB methods for very small times, we prove some instability phenomena for semi-classical (linear or) nonlinear Schrödinger equations. The main step of the analysis consists in reducing the problem to an ordinary differential equation. The solution to this o.d.e. is explicit, and the instability mechanism is due to the presence of the semi-classical parameter. For nonlin-ear equations, our...
متن کاملar X iv : h ep - p h / 06 08 02 5 v 1 2 A ug 2 00 6 SOLUTION TO THE LHC INVERSE PROBLEM
The " LHC Inverse Problem " refers to the question of determining the underlying physical theory giving rise to the signals expected to be seen at the Large Hadron Collider. The solution to this problem (Bard) is reviewed. The combination of CDF and DØ data is motivated. These proceedings explore the incorrectness of each of the three words in " LHC Inverse Problem. " We work backward. Sections...
متن کامل