Geometrical approach to inverse scattering for the Dirac equation

Abstract

Solution of the Dirac equation with pseudospin symmetry for a new harmonic oscillatory ring-shaped noncentral potential J. Math. Phys. 53, 082104 (2012) Effect of tensor interaction in the Dirac-attractive radial problem under pseudospin symmetry limit J. Math. Phys. 53, 082101 (2012) Asymptotic stability of small gap solitons in nonlinear Dirac equations J. Math. Phys. 53, 073705 (2012) On Dirac-Coulomb problem in (2+1) dimensional space-time and path integral quantization J. Math. Phys. 53, 063503 (2012) Quasi-exact treatment of the relativistic generalized isotonic oscillator The high-energy-limit of the scattering operator for multidimensional relativistic dynamics, including a Dirac particle in an electromagnetic field, is investigated by using time-dependent, geometrical methods. This yields a reconstruction formula, by which the field can be obtained uniquely from scattering data. © 1997 American Institute of Physics. ͓S0022-2488͑97͒02701-1͔

Aharonov–Bohm Effect and High-Momenta Inverse Scattering for the Klein–Gordon Equation

“…Similar results for non-obstacle relativistic-scattering are presented in [8,28]. There error bounds are not provided and a different class of (bounded) electromagnetic potentials is addressed.…”

“…In [3] and [31] one can see that the circulation of the magnetic potential appears on the leading order term of the high velocity asymptotic of the scattering operator, whereas the contribution of the electric potential appears only on the second order term (see [31] for related issues). For relativistic equations in the whole space, see [8] and [28]. The time dependent methods for inverse scattering that we use are introduced in [9], for the Schrödinger equation.…”

Recovering the mass and the charge of a Reissner–Nordström black hole by an inverse scattering experiment

“…This method can be used to study Hamiltonians with electric and magnetic potentials [1], the Dirac equation [21] and Stark Hamiltonians [31,27].…”

“…The strategy we adopt to prove our main result is based on a high-energy asymptotic expansion of the scattering operator S. Such a technique was introduced by Enss and Weder in [11] and used sucessfully to recover the potential of multidimensional Schrödinger operators (note that the case of multidimensional Dirac operators in flat spacetime was treated later by Jung in [21]). They showed that the first term of the high-energy asymptotics is exactly the Radon transform of the potential they are looking for.…”

An inverse scattering problem for short-range systems in a time-periodic electric field

“…This method can be used to study Hamiltonians with electric and magnetic potentials on L 2 (R n ) [1], the Dirac equation [9], the N-body case [4], the Stark effect ( [15], [17]), the AharonovBohm effect [18].…”