caa a22 4500 467911126 CHVBK 20180406152849.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s11232-006-0150-1 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0150-1 Quasi-exact solution of the problem of relativistic bound states in the (1+1)-dimensional case [Elektronische Daten] [K. Sveshnikov, P. Silaev] We investigate the problem of bound states for bosons and fermions in the framework of the relativistic configurational representation with the kinetic part of the Hamiltonian containing purely imaginary finite shift operators e±ihd/dx instead of differential operators. For local (quasi)potentials of the type of a rectangular potential well in the (1+1)-dimensional case, we elaborate effective methods for solving the problem analytically that allow finding the spectrum and investigating the properties of wave functions in a wide parameter range. We show that the properties of these relativistic bound states differ essentially from those of the corresponding solutions of the Schrödinger and Dirac equations in a static external potential of the same form in a number of fundamental aspects both at the level of wave functions and of the energy spectrum structure. In particular, competition between ℏ and the potential parameters arises, as a result of which these distinctions are retained at low-lying levels in a sufficiently deep potential well for ℏ ≪ 1 and the boson and fermion energy spectra become identical. Springer Science+Business Media, Inc., 2006 spectral problem in relativistic configurational representation nationallicence finite-difference equation nationallicence boson bound state nationallicence fermion bound state nationallicence Sveshnikov K. Moscow State University, Moscow, Russia aut Silaev P. Moscow State University, Moscow, Russia aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 149/3(2006-12-01), 1665-1689 0040-5779 149:3<1665 2006 149 11232 https://doi.org/10.1007/s11232-006-0150-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0150-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sveshnikov K. Moscow State University, Moscow, Russia aut NATIONALLICENCE 700 1- Silaev P. Moscow State University, Moscow, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 149/3(2006-12-01), 1665-1689 0040-5779 149:3<1665 2006 149 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer