Quantum Mechanical Angular Distributions and Group Representations on Banach Spaces

1981 ◽  
pp. 415-434
Author(s):  
Michael P. Strand ◽  
R. Stephen Berry
Keyword(s):  
Banach Spaces ◽  
Angular Distributions ◽  
Quantum Mechanical ◽  
Group Representations

Seemingly Anomalous Angular Distributions in H + D2 Reactive Scattering

Science ◽  
2012 ◽  
Vol 336 (6089) ◽  
pp. 1687-1690 ◽  
Author(s):  
Justin Jankunas ◽  
Richard N. Zare ◽  
Foudhil Bouakline ◽  
Stuart C. Althorpe ◽  
Diego Herráez-Aguilar ◽  
...  
Keyword(s):  
Cross Sections ◽  
Collision Energy ◽  
Minimum Energy ◽  
Angular Distributions ◽  
Quantum Mechanical ◽  
Minimum Energy Path ◽  
Reactive Scattering ◽  
Rotational Excitation ◽  
Reaction Products ◽  
Trajectory Calculations

When a hydrogen (H) atom approaches a deuterium (D2) molecule, the minimum-energy path is for the three nuclei to line up. Consequently, nearly collinear collisions cause HD reaction products to be backscattered with low rotational excitation, whereas more glancing collisions yield sideways-scattered HD products with higher rotational excitation. Here we report that measured cross sections for the H + D2 → HD(v′ = 4, j′) + D reaction at a collision energy of 1.97 electron volts contradict this behavior. The anomalous angular distributions match closely fully quantum mechanical calculations, and for the most part quasiclassical trajectory calculations. As the energy available in product recoil is reduced, a rotational barrier to reaction cuts off contributions from glancing collisions, causing high-j′ HD products to become backward scattered.

scholarly journals Disintegration of Group Representations on Direct Integrals of Banach Spaces

2019 ◽  
Vol 09 (11) ◽  
pp. 879-924
Author(s):  
Simon Joseph ◽  
Fatin Saeed ◽  
Nagat Suoliman ◽  
Mohammed Khanfoor ◽  
Abd Elmotaleb Abd Ellah
Keyword(s):  
Banach Spaces ◽  
Group Representations

scholarly journals Group representations in non-archimedean Banach spaces

1974 ◽  
Vol 1 ◽  
pp. 329-340 ◽  
Author(s):  
A. C. M. van Rooij ◽  
W. H. Schikhof
Keyword(s):  
Banach Spaces ◽  
Group Representations

Quantum mechanical angular distributions for the F+HD reaction

1998 ◽  
Vol 110 ◽  
pp. 119-138 ◽  
Author(s):  
Jesus F. Castillo ◽  
David E. Manolopoulos
Keyword(s):  
Angular Distributions ◽  
Quantum Mechanical

Quantum mechanical angular distributions for the F+H2 reaction

1996 ◽  
Vol 104 (17) ◽  
pp. 6531-6546 ◽  
Author(s):  
Jesus F. Castillo ◽  
David E. Manolopoulos ◽  
Klaus Stark ◽  
Hans‐Joachim Werner
Keyword(s):  
Angular Distributions ◽  
Quantum Mechanical

Banach spaces related to integrable group representations and their atomic decompositions. Part II

1989 ◽  
Vol 108 (2-3) ◽  
pp. 129-148 ◽  
Author(s):  
Hans G. Feichtinger ◽  
K. H. Gr�chenig
Keyword(s):  
Banach Spaces ◽  
Group Representations ◽  
Atomic Decompositions
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