ua nt - p h / 04 05 17 2 v 1 2 8 M ay 2 00 4 Scattering in highly singular potentials
نویسنده
چکیده
Recently, in Quantum Field theory, there has been an interest in scattering in highly singular potentials. Here, solutions to the stationary Schrödinger equation are presented when the potential is a multiple of an arbitrary positive power of the Dirac delta distribution. The one dimensional, and spherically symmetric three dimensional cases are dealt with. 1. One space dimension In Rosinger [4-6] solutions to the following stationary Schrödinger equations are given (1) d 2 dx 2 ψ(x) + (k − U(x)) ψ(x) = 0, x ∈ R for any k ∈ R, while the potentials U are scalar multiples of arbitrary positive powers of the Dirac delta distribution δ, that is (2) U(x) = c δ m (x), x ∈ R with c ∈ R and m > 0 chosen at will.
منابع مشابه
ua nt - p h / 04 05 07 2 v 1 1 3 M ay 2 00 4 s - ordered phase - sum and phase - difference distributions of entangled coherent states
The s-ordered phase-sum and phase-difference distributions are considered for Bell-like superpositions of two-mode coherent states. The distributions are sensitive, respectively, to the sum and difference of the phases of the entangled coherent states. They show loss of information about the entangled state and may take on negative values for some orderings s.
متن کاملua nt - p h / 02 05 18 4 v 1 2 9 M ay 2 00 2 Focusing of atoms with strongly confined light potentials
Focusing of atoms with light potentials is studied. In particular, we consider strongly confined, cylindrical symmetric potential, and demonstrate their applications in both red and blue-detuned focusing of atoms. We also study the influence of aberrations, and find that a resolution of 1 nm should in principle be possible.
متن کاملar X iv : q ua nt - p h / 04 05 01 1 v 1 3 M ay 2 00 4 Decoherence alias Loschmidt echo of the environment
T. Gorin, T. Prosen, T. H. Seligman, 4 and W. T. Strunz Theoretische Quantendynamik, Albert-Ludwigs-Universität, Hermann-Herder-Str. 3, 79104 Freiburg, Germany Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia Centro Internacional de Ciencias, C.P. 62131 Cuernavaca, Morelos Mexico Centro de Ciencias F́ısicas, University of ...
متن کاملar X iv : q ua nt - p h / 04 05 11 6 v 1 2 0 M ay 2 00 4 Complementarity of Entanglement and Interference
A complementarity relation is shown between the visibility of interference and bipartite entanglement in a two qubit interferometric system when the parameters of the quantum operation change for a given input state. The entanglement measure is a decreasing function of the visibility of interference. The implications for quantum computation are briefly discussed.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004