Bound states of (2 + 1)-dimensional massive Dirac fermions in a Lorentzian-shaped inhomogeneous perpendicular magnetic field: Supplementary Materials Dai-Nam Le a,b , Phong-Su Luu c , Thanh-Sang Ha c , Ngoc-Hung Phan c , Van-Hoang Le c,a a Atomic Molecular and Optical Physics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam b Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam c Department of Physics, Ho Chi Minh City University of Education, 280 An Duong Vuong Street, District 5, Ho Chi Minh City, Vietnam 1. Results in conditional harmonic confinement case Table 1: Numerical values of β 1 , which allow condi- tional harmonic solutions, are calculated from Eq. (22) when λ = 1 and N = 1 and the corresponding allowed states (n, m) with their energy En,m. β 1 (n, m) energy 0.10000000E+01 (0, -1) ±0.57445626E+01 (1, -1) ±0.60827625E+01 (2, -1) ±0.64031242E+01 (3, -1) ±0.67082039E+01 (4, -1) ±0.70000000E+01 0.14142136E+01 (0, -2) ±0.60827625E+01 (1, -2) ±0.64031242E+01 (2, -2) ±0.67082039E+01 (3, -2) ±0.70000000E+01 (4, -2) ±0.72801099E+01 0.17320508E+01 (0, -3) ±0.64031242E+01 (1, -3) ±0.67082039E+01 (2, -3) ±0.70000000E+01 (3, -3) ±0.72801099E+01 (4, -3) ±0.75498344E+01 0.20000000E+01 (0, -4) ±0.67082039E+01 (1, -4) ±0.70000000E+01 (2, -4) ±0.72801099E+01 (3, -4) ±0.75498344E+01 (4, -4) ±0.78102497E+01 0.22360680E+01 (0, -5) ±0.70000000E+01 (1, -5) ±0.72801099E+01 (2, -5) ±0.75498344E+01 (3, -5) ±0.78102497E+01 (4, -5) ±0.80622577E+01 Table 2: Numerical values of β 1 and β 2 , which allow conditional har- monic solutions, are calculated from Eq. (22) when λ = 1 and N =2 and the corresponding allowed states (n, m) with their energy En,m. β 1 β 2 (n, m) energy 0.76536686E+00 0.18477591E+01 (0, -1) ±0.60827625E+01 (1, -1) ±0.64031242E+01 (2, -1) ±0.67082039E+01 (3, -1) ±0.70000000E+01 (4, -1) ±0.72801099E+01 0.11260325E+01 0.21753277E+01 (0, -2) ±0.64031242E+01 (1, -2) ±0.67082039E+01 (2, -2) ±0.70000000E+01 (3, -2) ±0.72801099E+01 (4, -2) ±0.75498344E+01 0.14142136E+01 0.24494897E+01 (0, -3) ±0.67082039E+01 (1, -3) ±0.70000000E+01 (2, -3) ±0.72801099E+01 (3, -3) ±0.75498344E+01 (4, -3) ±0.78102497E+01 0.16625078E+01 0.26899940E+01 (0, -4) ±0.70000000E+01 (1, -4) ±0.72801099E+01 (2, -4) ±0.75498344E+01 (3, -4) ±0.78102497E+01 (4, -4) ±0.80622577E+01 0.18842798E+01 0.29068006E+01 (0, -5) ±0.72801099E+01 (1, -5) ±0.75498344E+01 (2, -5) ±0.78102497E+01 (3, -5) ±0.80622577E+01 (4, -5) ±0.83066239E+01 Email addresses: ledainam@tdtu.edu.vn (Dai-Nam Le), hoanglv@hcmup.edu.vn (Van-Hoang Le) Preprint submitted to Elsevier August 30, 2019