few-body problem; Schroedinger and Faddeev equations; elliptic equations; solution in closed form; asymptotic behavior of solutions; asymptotic and functional expansions.
Subject:
For a complete study of the one-dimensional Schoedinger scattering problem with the sum of the Coulomb potential and a potential, decreasing more rapidly than the centrifugal one, perturbation theory is constructed within the linear version of the variable phase approach. The theory suggested is the asymptotic method in the low-energy limit and in a large angular momentum limit. A number of papers were devoted to investigation of the construction of three-particle wave functions. These investigations are performed within the Schroedinger and Faddeev differential equations in the six-dimensional configuration space. An unified method to construct the complete asymptotic expansions of the wave functions in the vicinity of the double and triple collision points and nearly the line, connected two particles, was proposed. The criterion for existence of three-particles spurious solutions and spurious terms was established. Exact solutions of the three-body problem with pairwise interactions inversely proportional square distance was constructed. The criterion for existence of such solutions was proved. The sufficient condition for the three-body collapse was obtained.
Biography
Graduated from Physical Faculty of M. V. Lomonosov Moscow State University (MSU) in 1979 (department of theoretical nuclear physics). Ph.D. thesis was defined in 1983. A list of my works contains more than 70 titles.
Main publications:
Pupyshev V. V. Asymptotic Expansions of Wave Functions of Three Identical Particles for Small Hyperradius and S-Wave Potentials // Few-Body Systems, 1990, 8, 105–122.
V. V. Pupyshev, “Low-energy asymptotics of the phases of two-dimensional scattering of
a quantum particle by a central long-range potential”, TMF, 207:1 (2021), 72–98; Theoret. and Math. Phys., 207:1 (2021), 459–482
V. V. Pupyshev, “Two-dimensional low-energy scattering of a quantum particle in the summed field of Coulomb and power-law potentials”, TMF, 203:2 (2020), 280–299; Theoret. and Math. Phys., 203:2 (2020), 673–690
2019
3.
V. V. Pupyshev, “Two-dimensional motion of a slow quantum particle in the field of a central long-range potential”, TMF, 199:3 (2019), 405–428; Theoret. and Math. Phys., 199:3 (2019), 828–848
V. V. Pupyshev, “Coulomb scattering of a slow quantum particle in a space of
arbitrary dimension”, TMF, 195:1 (2018), 64–74; Theoret. and Math. Phys., 195:1 (2018), 548–556
V. V. Pupyshev, “Two-dimensional nuclear Coulomb scattering of a slow quantum
particle”, TMF, 193:2 (2017), 225–255; Theoret. and Math. Phys., 193:2 (2017), 1602–1629
6.
V. V. Pupyshev, “The method of amplitude functions in two-dimensional scattering
theory”, TMF, 191:1 (2017), 34–62; Theoret. and Math. Phys., 191:1 (2017), 499–523
V. V. Pupyshev, “Two-dimensional Coulomb scattering of a quantum particle: Low-energy asymptotic behavior”, TMF, 188:1 (2016), 49–75; Theoret. and Math. Phys., 188:1 (2016), 1006–1029
V. V. Pupyshev, “Two-dimensional Coulomb scattering of a quantum particle: Wave functions and Green's functions”, TMF, 186:2 (2016), 252–271; Theoret. and Math. Phys., 186:2 (2016), 213–230
V. V. Pupyshev, “Two-dimensional Coulomb scattering of a quantum particle: Construction of radial wave functions”, TMF, 186:1 (2016), 123–141; Theoret. and Math. Phys., 186:1 (2016), 101–117
V. V. Pupyshev, “Effective-radius approximation in the problem of two-dimensional scattering by a central short-range potential”, TMF, 182:2 (2015), 315–337; Theoret. and Math. Phys., 182:2 (2015), 264–283
V. V. Pupyshev, “The length and effective radius of two-dimensional scattering of a quantum particle by a centrally symmetric short-range potential”, TMF, 180:3 (2014), 342–367; Theoret. and Math. Phys., 180:3 (2014), 1051–1072
V. V. Pupyshev, “Energies of weakly bound and near-threshold resonance states of a quantum particle in a two-dimensional plane”, TMF, 179:1 (2014), 102–122; Theoret. and Math. Phys., 179:1 (2014), 472–489
V. V. Pupyshev, “Structure of regular solutions of Faddeev equations near the pair
impact point”, TMF, 156:1 (2008), 112–130; Theoret. and Math. Phys., 156:1 (2008), 1058–1074
14.
V. V. Pupyshev, “Construction of regular solutions of Schrödinger and Faddeev
equations in the linear three-particle configuration limit”, TMF, 155:3 (2008), 415–438; Theoret. and Math. Phys., 155:3 (2008), 862–883
V. V. Pupyshev, “Spurious solutions of three-dimensional Faddeev equations”, TMF, 148:2 (2006), 227–242; Theoret. and Math. Phys., 148:2 (2006), 1067–1080
V. V. Pupyshev, “Extrapolation of the differential cross section for triplet <i>pp</i> scattering to low energies”, Pis'ma v Zh. Èksper. Teoret. Fiz., 82:5 (2005), 275–278; JETP Letters, 82:5 (2005), 243–247
V. V. Pupyshev, “Structure of Regular Solutions of the Three-Body Schrödinger Equation near the Pair Impact Point”, TMF, 136:1 (2003), 90–114; Theoret. and Math. Phys., 136:1 (2003), 970–993
V. V. Pupyshev, “Three-Particle Problem with Pairwise Interactions Inversely Proportional to Squared Distance”, TMF, 128:2 (2001), 268–287; Theoret. and Math. Phys., 128:2 (2001), 1061–1077
V. V. Pupyshev, “Spurious solutions of Faddeev equations with central potentials”, TMF, 107:3 (1996), 501–512; Theoret. and Math. Phys., 107:3 (1996), 825–834
V. V. Pupyshev, “Perturbation theory for the one-dimensional Schrödinger scattering problem”, TMF, 105:1 (1995), 29–45; Theoret. and Math. Phys., 105:1 (1995), 1210–1223
1989
22.
V. V. Pupyshev, “On three-particle integrodifferential equations”, TMF, 81:1 (1989), 86–93; Theoret. and Math. Phys., 81:1 (1989), 1072–1077
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