New solutions for graphene with scalar potentials by means of generalized intertwining
Saint Petersburg State University, 7/9 Universitetskaya nab., 199034, St.Petersburg, Russia
2 Akaki Tsereteli State University, 4600, Kutaisi, Georgia
* e-mail: firstname.lastname@example.org
Accepted: 4 June 2019
Published online: 17 September 2019
The intertwining relations between superpartner Hamiltonians are the main ingredients of well-known Supersymmetrical Quantum Mechanics (SUSY QM). In the present paper, the generalized form of intertwining is used for the investigation of a massless (zero energy) two-dimensional Dirac equation with scalar external potential. This equation is related to the description of graphene and some other materials in the field of external electrostatic potential. The use of modified intertwining relations allows to find analytically solutions for the wave functions in the field of some external scalar potentials which depend on both space coordinates. A few examples of this construction are given explicitly.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019