Сoordinate and momentum tunneling in one-dimensional quantum systems with discrete spectrum

Semjon A. Vugalter, G. M. Zhislin

H. N. Núñez‐Yépez, Carlos Alejandro Vargas, A. L. Salas Brito

A momentum representation treatment of the one-dimensional hydrogen atom with Coulomb interaction is presented. The authors obtain the energy levels and bound-state eigenfunctions for the problem and discuss the general properties of the solution. The energy spectrum is discrete and given by the Balmer formula. They show that, despite the symmetry of the potential, it is impossible to find eigenfunctions with definite parity for the system.

G. Levin, Wesley Jones, Kamil Walczak +1 more

Sadulla Mamarazhabovich Tashpulatov, R. T. Parmanova

We consider the energy operator of four-electron systems in an impurity Hubbard model and investigated the structure of essential spectra and discrete spectrum of the system in the first triplet state in a one-dimensional lattice. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model. The investigations show that there are such cases: 1) the essential spectrum of the system consists of the union of no more than eight segments, and the discrete spectrum of the system consists of no more than three eigenvalues; 2) the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues; 3) the essential spectrum of the system consists of the union of no more than three segments, and the discrete spectrum of the system is the empty set. Consequently, the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.

Yasuhiro Saiga, Shinji Watanabe, Yoshio Kuramoto +3 more

M. A. Antonets, G. M. Zhislin, Ilya A. Shereshevskii