Scattering by a separable potential in one dimension

1990 ◽  
Vol 68 (4-5) ◽  
pp. 403-410 ◽  
Author(s):  
J. G. Muga ◽  
R. F. Snider
Keyword(s):  
Phase Shift ◽  
Partial Wave Analysis ◽  
Three Dimensions ◽  
One Dimension ◽  
Separable Potential ◽  
Wave Analysis ◽  
S Matrix ◽  
Low Energies ◽  
Reflectance Coefficient ◽  
Excess Density

The scattering by a separable potential in one dimension is described by means of explicit expressions for the reflectance coefficient, phase shift, and excess density. Resonances, bound and virtual states are analyzed in the light of the position of the poles of the resolvent, and a physical consequence of the spurious poles of the S matrix is indicated. Deviations from the usual partial wave analysis in three dimensions, especially a modification of Levinson's theorem, are also studied. It is shown that at very low energies the slope of the phase shift is not always a valid indicator of the excess density in the interaction region.

Transition from discrete to continuous spectrum: separable potential in one dimension

1990 ◽  
Vol 68 (4-5) ◽  
pp. 394-402 ◽  
Author(s):  
J. G. Muga ◽  
R. F. Snider
Keyword(s):  
Perturbation Theory ◽  
Phase Shift ◽  
Continuous Spectrum ◽  
Wave Functions ◽  
Phase Factor ◽  
One Dimension ◽  
Separable Potential ◽  
Level Shift ◽  
Momentum Representation ◽  
Convergence Parameter

An analysis is made of the transition from the discrete to the continuous spectrum for a separable potential in one dimension. The role played by the length of the box and the convergence parameter, ε, in the different limiting operations is discussed. Relations are found between scattering and perturbation theory matrices and wave functions in momentum representation. In particular, the known expression relating the level shift to the phase shift is recovered. The scattering and Brillouin–Wigner perturbation wave functions are in general not simply related by a phase factor.

scholarly journals SCATTERING PHASE SHIFTS IN QUASI-ONE-DIMENSION

2002 ◽  
Vol 16 (16) ◽  
pp. 2247-2277 ◽  
Author(s):  
P. SINGHA DEO ◽  
SWARNALI BANDOPADHYAY ◽  
SOURIN DAS
Keyword(s):  
Quantum Wires ◽  
Phase Shifts ◽  
Three Dimensions ◽  
One Dimension ◽  
Sum Rule ◽  
S Matrix ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Scattering Matrix Elements ◽  
Arbitrary Energy

Scattering of an electron in quasi-one-dimensional quantum wires have many unusual features, not found in one, two or three-dimensions. In this work we analyze the scattering phase shifts due to an impurity in a multi-channel quantum wire with special emphasis on negative slopes in the scattering phase shift versus incident energy curves and the Wigner delay time. Although at first sight, the large number of scattering matrix elements show phase shifts of different character and nature, it is possible to see some pattern and understand these features. The behavior of scattering phase shifts in one-dimension can be seen as a special case of these features observed in quasi-one-dimensions. The negative slopes can occur at any arbitrary energy and Friedel sum rule is completely violated in quasi-one-dimension at any arbitrary energy and any arbitrary regime. This is in contrast to one, two or three dimensions where such negative slopes and violation of Friedel sum rule happen only at low energy where the incident electron feels the potential very strongly (i.e. there is a very well defined regime, the WKB regime, where FSR works very well). There are some novel behavior of scattering phase shifts at the critical energies where S-matrix changes dimension.

Proton collisions with hydrogen atoms at low energies: quantum theory and integrated cross-sections

1977 ◽  
Vol 353 (1675) ◽  
pp. 575-588 ◽  
Keyword(s):  
Quantum Theory ◽  
Cross Sections ◽  
Phase Shifts ◽  
State Theory ◽  
Partial Wave Analysis ◽  
Quantum Mechanical ◽  
Wave Analysis ◽  
Hydrogen Atoms ◽  
Proton Collisions ◽  
Low Energies

Cross-sections for collisions of protons with hydrogen atoms have been computed by partial wave analysis within the perturbed stationary state theory. Phase shifts with 6 decimal accuracy were obtained by the use of adiabatically corrected 1Sσ g and 2Pσ u H + 2 potentials together with accurate numerical methods. The phase shifts and the integrated cross-sections derived from them are reported for 57 values of the energy ranging from 0.0001 eV (1.2 K) to 10 eV. These accurate quantum mechanical results differ from semi-classical results especially at energies below 0.1 eV.

Bonding and stability in the ordered alloys FeV and CoTi. Comparison with FeTi

1985 ◽  
Vol 50 (10) ◽  
pp. 2093-2100
Author(s):  
Štěpán Pick ◽  
Mojmír Tomášek ◽  
Mojmír Šob
Keyword(s):  
Phase Diagrams ◽  
Partial Wave ◽  
Partial Wave Analysis ◽  
Intermetallic Alloys ◽  
Wave Analysis ◽  
Ordered Alloys ◽  
Ordered Intermetallic ◽  
Cscl Structure ◽  
Ionic Effects

Partial wave analysis together with the qualitative examination of hybridization has been performed for two ordered intermetallic alloys with CsCl structure, FeV, and CoTi. The results resemble those obtained previously for FeTi, although important deviations are present as well. The stabilization of the ordered phase is again due to ionic effects. Qualitative arguments are suggested to explain the small stability of the CsCl phase of FeV and some differences in the FeTi and CoTi phase diagrams.

scholarly journals Partial Wave Analysis of $$\pmb {K^+N}$$ Scattering and the Possibility of Pentaquark $$\pmb {\Theta ^+(1540)}$$

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Kook-Jin Kong ◽  
Byung-Geel Yu
Keyword(s):  
Partial Wave ◽  
Partial Wave Analysis ◽  
Wave Analysis

scholarly journals Beyond-mean-field crossover from one dimension to three dimensions in quantum droplets of binary mixtures

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
L. Lavoine ◽  
T. Bourdel
Keyword(s):  
Binary Mixtures ◽  
Mean Field ◽  
Three Dimensions ◽  
One Dimension

New data on the reaction K−p→Λπ0 from 1.934 to 2.516 GeV/c and partial-wave analysis for this reaction between 2070 MeV and 2436 MeV CMS energy

1975 ◽  
Vol 90 ◽  
pp. 1-19 ◽  
Author(s):  
A. de Bellefon ◽  
A. Berthon ◽  
J. Brunet ◽  
G. Tristram ◽  
J. Vrana ◽  
...  
Keyword(s):  
Partial Wave ◽  
Partial Wave Analysis ◽  
Wave Analysis

Dielectric and Mechanical Loading Effects of a Fluid on Lamb Waves Propagating in an Immersed Piezoelectric Plate

2005 ◽  
Vol 21 (3) ◽  
pp. 179-186 ◽  
Author(s):  
C.-H. Yang ◽  
Y.-A. Lai
Keyword(s):  
Lamb Waves ◽  
Piezoelectric Plate ◽  
Dispersion Curves ◽  
Partial Wave Analysis ◽  
Theoretical Treatment ◽  
Fluid Loading ◽  
Wave Analysis ◽  
Sensor Applications ◽  
Dielectric Loading ◽  
Loading Effects

AbstractThis research is focused on exploring the fluid loading effects on the dispersion curves of Lamb modes propagating in a piezoelectric plate. A theoretical treatment based on a partial wave analysis is developed to model the dispersion curves of Lamb modes propagating in an X-LiNbO3 plate loaded by a fluid with combined mechanical/dielectric properties. In particular, the mode-shifting characteristics caused by the fluid loading as a function of the propagation orientation are illustrated with numerical examples. Finally, for the case of water as an immersing fluid, individual attributions of the mechanical and dielectric loading effects causing the mode-shifting are analyzed. It is found that the dielectric loading effect dominates the mode-shifting while the mechanical density loading can be neglected while Lamb waves propagate in an X-LiNbO3 plate immersing in water. The current results provides useful information for the applications of acoustic plate mode (APM) devices used in liquid sensor applications.

Partial-wave analysis of K−p → π0Λ (1520) between 1710 and 2170 MeV c.m. energy including new data between 1775 and 1960 MeV

1977 ◽  
Vol 131 (4-5) ◽  
pp. 399-420 ◽  
Author(s):  
W. Cameron ◽  
B. Franek ◽  
G.P. Gopal ◽  
G.E. Kalmus ◽  
A.C. McPherson ◽  
...  
Keyword(s):  
Partial Wave ◽  
Partial Wave Analysis ◽  
Wave Analysis
Sign in / Sign up

Export Citation Format

Share Document