Yazar "Uncu, Haydar" seçeneğine göre listele

Listeleniyor 1 - 2 / 2
  • [ X ]
    Öğe
    THE CONSTRUCTION OF GEL'FAND TRIPLET SPACE STRUCTURE FOR INFINITE POTENTIAL WELL SYSTEM
    (Pergamon-Elsevier Science Ltd, 2023) Genc, Onur; Uncu, Haydar
    The Hilbert space is the space which is usually chosen as the space of state vectors. In addition, the operators of quantum mechanics act on that space. However, the Hilbert space cannot provide a proper mathematical structure to define Dirac formulation. In particular, the use of Dirac formalism on the domain of definition of an observable leads to some physical contradictions. One example arises from the Infinite Potential Well System (IPWS) which is one of the most fundamental systems of quantum mechanics. Our aim in this paper is the explicit construction of the Gel'fand triplet for the IPWS.
  • [ X ]
    Öğe
    The harmonic oscillator potential perturbed by a combination of linear and non-linear Dirac delta interactions with application to Bose-Einstein condensation
    (Elsevier, 2024) Akyuz, Cenk; Erman, Fatih; Uncu, Haydar
    In this paper, we study the bound state analysis of a one dimensional nonlinear version of the Schrodinger equation for the harmonic oscillator potential perturbed by a delta potential, where the nonlinear term is taken to be proportional to delta(x)vertical bar psi(x)vertical bar(2) psi(x). The bound state wave functions are explicitly found and the bound state energy of the system is algebraically determined by the solution of an implicit equation. Then, we apply this model to the Bose-Einstein condensation of a Bose gas in a harmonic trap with a dimple potential. We propose that the many-body interactions of the Bose gas can be effectively described by the nonlinear term in the Schrodinger equation. Then, we investigate the critical temperature, the condensate fraction, and the density profile of this system numerically.