Relativistic and nonrelativistic models in one dimension which simulate the deuteron and the $^{3}\mathrm{S}_{1}$ nucleon-nucleon (NN) scattering are constructed and the relation between the scattering length ${a}_{t}$ and the root-mean-square radius ${r}_{m}$ of the simulated deuteron is examined for a variety of interactions. The linear relation between ${a}_{t}$ and ${r}_{m}$ , which was found by Klarsfeld et al. for realistic NN potentials, holds for a wide class of potentials, relativistic as well as nonrelativistic. Within the limitation of our one-dimensional models, this suggests that the discrepancy between theory and experiment which was pointed out by Klarsfeld et al. regarding ${a}_{t}$ and ${r}_{m}$ cannot be resolved by relativistic effects.Relativistic and nonrelativistic models in one dimension which simulate the deuteron and the $^{3}\mathrm{S}_{1}$ nucleon-nucleon (NN) scattering are constructed and the relation between the scattering length ${a}_{t}$ and the root-mean-square radius ${r}_{m}$ of the simulated deuteron is examined for a variety of interactions. The linear relation between ${a}_{t}$ and ${r}_{m}$, which was found by Klarsfeld et al. for realistic NN potentials, holds for a wide class of potentials, relativistic as well as nonrelativistic. Within the limitation of our one-dimensional models, this suggests that the discrepancy between theory and experiment which was pointed out by Klarsfeld et al. regarding ${a}_{t}$ and ${r}_{m}$ cannot be resolved by relativistic effects.

Physical Review CDec 1, 19888 citations

One-Dimensional Potentials

Tapan Kumar Das

UNITEXT for physicsJan 1, 20230 citations

Bound states and scattering from a one-dimensional hydrogen atom at a boundary

I. Richard Lapidus

The bound-state energy of a one-dimensional hydrogen atom with a δ-function potential is modified by the presence of a nearby boundary. The distortion of the wave function raises the energy of the atom. If the atom is sufficiently close to a high barrier the system does not have a bound state. Scattering from a δ-function potential is also modified by the presence of the boundary. This simple example, which can be solved exactly, may help to provide insight into more realistic interactions between single atoms and surfaces.The bound-state energy of a one-dimensional hydrogen atom with a δ-function potential is modified by the presence of a nearby boundary. The distortion of the wave function raises the energy of the atom. If the atom is sufficiently close to a high barrier the system does not have a bound state. Scattering from a δ-function potential is also modified by the presence of the boundary. This simple example, which can be solved exactly, may help to provide insight into more realistic interactions between single atoms and surfaces.

American Journal of PhysicsDec 1, 19835 citations

Simple one-dimensional potentials

Sourendu Gupta A

Jan 1, 20130 citations

Trapped-atom interferometer in a magnetic microtrap

W. Hänsel, Jakob Reichel, Peter Hommelhoff +1 more

We propose a configuration of a magnetic microtrap that can be used as an interferometer for three-dimensionally trapped atoms. The interferometer is realized via a dynamic splitting potential that transforms from a single well into two separate wells and back. The ports of the interferometer are neighboring vibrational states in the single-well potential. We present a one-dimensional model of this interferometer and compute the probability of unwanted vibrational excitations for a realistic magnetic potential. We optimize the speed of the splitting process in order to suppress these excitations, and conclude that such interferometer device should be feasible with currently available microtrap technique.We propose a configuration of a magnetic microtrap that can be used as an interferometer for three-dimensionally trapped atoms. The interferometer is realized via a dynamic splitting potential that transforms from a single well into two separate wells and back. The ports of the interferometer are neighboring vibrational states in the single-well potential. We present a one-dimensional model of this interferometer and compute the probability of unwanted vibrational excitations for a realistic magnetic potential. We optimize the speed of the splitting process in order to suppress these excitations, and conclude that such interferometer device should be feasible with currently available microtrap technique.

arXiv:quant-ph/0106162Physical Review ANov 14, 2001137 citations

One-Dimensional Piecewise-Constant Potentials

Jochen Pade

Undergraduate lecture notes in physicsNov 7, 20130 citations

Relativistic and nonrelativistic models in one dimension which simulate the deuteron and the

^{3}\mathrm{S}_{1}

nucleon-nucleon (NN) scattering are constructed and the relation between the scattering length

{a}_{t}

and the root-mean-square radius

{r}_{m}

of the simulated deuteron is examined for a variety of interactions. The linear relation between

{a}_{t}

and

{r}_{m}

, which was found by Klarsfeld et al. for realistic NN potentials, holds for a wide class of potentials, relativistic as well as nonrelativistic. Within the limitation of our one-dimensional models, this suggests that the discrepancy between theory and experiment which was pointed out by Klarsfeld et al. regarding

{a}_{t}

and

{r}_{m}

cannot be resolved by relativistic effects.