Phase‐Integral Approximation in Momentum Space and the Bound States of an Atom. II

1969 ◽  
Vol 10 (6) ◽  
pp. 1004-1020 ◽  
Author(s):  
Martin C. Gutzwiller
Keyword(s):  
Momentum Space ◽  
Bound States ◽  
Integral Approximation ◽  
Phase Integral

Phase‐Integral Approximation in Momentum Space and the Bound States of an Atom

1967 ◽  
Vol 8 (10) ◽  
pp. 1979-2000 ◽  
Author(s):  
Martin C. Gutzwiller
Keyword(s):  
Momentum Space ◽  
Bound States ◽  
Integral Approximation ◽  
Phase Integral

scholarly journals Comments on ’’Higher order modified potentials for the effective phase integral approximation’’

1981 ◽  
Vol 22 (6) ◽  
pp. 1190-1191 ◽  
Author(s):  
Nanny Fröman ◽  
Per Olof Fröman
Keyword(s):  
Higher Order ◽  
Integral Approximation ◽  
Phase Integral ◽  
Effective Phase

Two classes of special functions for the phase-integral approximation

1979 ◽  
Vol 12 (8) ◽  
pp. 1149-1154 ◽  
Author(s):  
J A Campbell
Keyword(s):  
Special Functions ◽  
Integral Approximation ◽  
Phase Integral

Transmission through cutoffs and resonances in the double phase‐integral approximation

1984 ◽  
Vol 25 (9) ◽  
pp. 2655-2661 ◽  
Author(s):  
Andrzej A. Skorupski
Keyword(s):  
Integral Approximation ◽  
Double Phase ◽  
Phase Integral

A large-N phase integral approximation of Coulomb-type systems using SO(2,1) coherent states

1986 ◽  
Vol 19 (18) ◽  
pp. 3797-3806 ◽  
Author(s):  
C C Gerry ◽  
J B Togeas
Keyword(s):  
Coherent States ◽  
Type Systems ◽  
Integral Approximation ◽  
Large N ◽  
Coulomb Type ◽  
Phase Integral

scholarly journals Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum

2020 ◽  
Vol 14 (10) ◽  
pp. 623-628 ◽  
Author(s):  
Bo Wang ◽  
Wenzhe Liu ◽  
Maoxiong Zhao ◽  
Jiajun Wang ◽  
Yiwen Zhang ◽  
...  
Keyword(s):  
Momentum Space ◽  
Bound States ◽  
Optical Vortex ◽  
Vortex Beams ◽  
Space Polarization ◽  
The Continuum

Coulomb plus strong interaction bound states - momentum space numerical solutions

1985 ◽  
Vol 38 (1) ◽  
pp. 71-82 ◽  
Author(s):  
David P. Heddle ◽  
Yong Rae Kwon ◽  
F. Tabakin
Keyword(s):  
Strong Interaction ◽  
Momentum Space ◽  
Bound States ◽  
Numerical Solutions

scholarly journals Floquet Second-Order Topological Phases in Momentum Space

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1170
Author(s):  
Longwen Zhou
Keyword(s):  
Momentum Space ◽  
Bound States ◽  
Second Order ◽  
Large Integer ◽  
Open Boundary ◽  
Topological Invariants ◽  
Topological Phases ◽  
Open Boundary Conditions ◽  
Kicked Rotor ◽  
Symmetry Protected

Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are demonstrated in a two-dimensional extension of the quantum double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry and characterized by a pair of topological invariants, which could take arbitrarily large integer values with the increase of kicking strengths. These topological numbers are shown to be measurable from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and π quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in the continuum. The number of these corner modes is further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study of HOTPs to momentum-space lattices and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet systems.

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