TY - JOUR
T1 - Asymptotic and numerical analysis of slowly varying two-dimensional quantum waveguides
AU - Barrera-Figueroa, Víctor
AU - Rabinovich, Vladimir S.
AU - Cristina Loredo-Ramírez, Samantha Ana
N1 - Publisher Copyright:
© 2022 IOP Publishing Ltd.
PY - 2022/3/4
Y1 - 2022/3/4
N2 - The work is devoted to the asymptotic and numerical analysis of the wave function propagating in two-dimensional quantum waveguides with confining potentials supported on slowly varying tubes. The leading term of the asymptotics of the wave function is determined by an adiabatic approach and the WKB approximation. Unlike other similar studies, in the present work we consider arbitrary bounded potentials and obtain exact solutions for the thresholds, and for the transverse modes in the form of power series of the spectral parameter. Our approach leads to an effective numerical method for the analysis of such quantum waveguides and for the tunnel effect observed in sections of the waveguide that shrink or widen too much. Several examples of interest show the applicability of the method.
AB - The work is devoted to the asymptotic and numerical analysis of the wave function propagating in two-dimensional quantum waveguides with confining potentials supported on slowly varying tubes. The leading term of the asymptotics of the wave function is determined by an adiabatic approach and the WKB approximation. Unlike other similar studies, in the present work we consider arbitrary bounded potentials and obtain exact solutions for the thresholds, and for the transverse modes in the form of power series of the spectral parameter. Our approach leads to an effective numerical method for the analysis of such quantum waveguides and for the tunnel effect observed in sections of the waveguide that shrink or widen too much. Several examples of interest show the applicability of the method.
KW - Green function
KW - Wentzel-Kramers-Brillouin (WKB) approximation
KW - adiabatic approach
KW - slowly varying tube
KW - spectral parameter power series (SPPS) method
KW - tunnel effect
KW - wave function
UR - http://www.scopus.com/inward/record.url?scp=85124431332&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/ac4b14
DO - 10.1088/1751-8121/ac4b14
M3 - Artículo
AN - SCOPUS:85124431332
SN - 1751-8113
VL - 55
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 9
M1 - 095202
ER -