PARTICLE DENSITY IN THE ONE-DIMENSIONAL SYSTEM OF BOSON WITH delta LIKE ATTRACTIVE POTENTIAL

J. C. Garrison, J. S. W. Wong

B. Basu-Mallick, Tanaya Bhattacharyya

We investigate the boson–fermion duality relation for the case of quantum integrable derivative δ-function Bose gas. In particular, we find a dual fermionic system with nonvanishing zero-range interaction for the simplest case of two bosonic particles with derivative δ-function interaction. The coupling constant of this dual fermionic system becomes inversely proportional to the product of the coupling constant of its bosonic counterpart and the center-of-mass momentum of the corresponding eigenfunction.

Chan Hong-Mo, Jean G. Valatin

L. V. Belvedere, R. L. P. G. Amaral, A. F. DE QUEIROZ

The effective Lagrangian model for charge-density waves interacting with an impurity potential in one-dimensional systems is considered in the dynamical phonon phase approach. Using the fermion–boson mapping we obtain the effective bosonized version of the model. The impurity potential breaks the linked electron–phonon symmetry, the phason field turns out to be in interaction with the electron–phonon condensate and the phonon field develops a non-vanishing vacuum expectation value. The effective fermionized version of the model corresponds to the chiral Gross–Neveu model with quartic self-interaction among a massless and a massive (electron) Fermi fields. The electron–phonon system exhibits a conserved topological charge which is independent of local variations of the phases of the phonon and electron fields. The equation of state of the associated statistical-mechanical system is obtained. For the dynamical phonon phase field the Kosterlitz–Thouless phase transition is suppressed.

K. K. Singh, Jai Prakash

Mukhtarov Erkin Kobilzhonovich

It is impossible for students to master the basic ideas and conclusions of quantum mechanics without solving a certain set of problems. Problems play a significant role in the educational process, forming not only logical thinking, but also influencing the overall development of the students. The article poses and solves problems about stationary one-dimensional problems in quantum mechanics.