Study of Bohr–Mottelson with minimal length effect for Q-deformed modified Eckart potential and Bohr–Mottelson with Q-deformed quantum for three-dimensional harmonic oscillator potential

Study of Bohr Mottelson Hamiltonian with minimal length effect for Woods-Saxon potential and its thermodynamic properties

“…According to string theory, ̂and ̂s hown in equation ( 6) are momentum operator at low energy and momentum operator at high energy, respectively. The squared of the momentum operator at low energy is formed by [24] 2 = −ℏ 2 Δ (7)…”

“…By substituting equation ( 14) into equation (24), the Bohr Mottelson Hamiltonian equation for the certain energy potential ( ) is given by…”

“…The deformed uncertainty of canonical commutation relation leads to the deformed uncertainty relation expressed as From equation (3) , we have the minimal length formulation The position and the momentum operators commute each other, that is According to string theory, and shown in equation (6) are momentum operator at low energy and momentum operator at high energy, respectively. The squared of the momentum operator at low energy is formed by [24] while, by substituting equation (7) into equation (6) will be obtained the squared of the momentum operator at high energy, given as where Δ is the Laplacian operator. The Laplacian operator for a nucleus has the form with g is the determinant of the matrix and is the inverse of the matrix .…”

“…Different potential models have been applied in the Bohr Mottelson equations such as infinite square well potential [17] , [21] , Morse potential [22] , [23] , Kratzer potential [5] , [23] , Davidson potential [10] , Eckart potential [24] , [25] , Woods–Saxon [26] , Hulthen potential [27] , etc. Various methods have been used to solve The Bohr Mottelson Hamiltonian equation with different potentials, such as the Nikiforov-Uvarov method [9] , Asymptotic Iteration Method [28] , and Supersymmetric quantum mechanics method [24] .…”

“…By considering the deformed canonical commutation relation, the minimal length concept can be incorporated in the study of the physical systems [41] . The Bohr Mottelson Hamiltonian equation with minimal length effect has been studied by Chabab et al [41] , Alimohammadi and Hassanabadi [7] , Hassanabadi et al [42] , and Suparmi et al [24] for certain potential models. The potential model used in the Bohr Mottelson equation within the minimal length formalism that has been solved was infinite square well potential either solved approximately using new wave function [41] or using alternative solution [7] .…”