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CAN THE TRANSMISSION LINE MATRIX METHOD YIELD STATIONARY SOLUTIONS OF THE TIME‐DEPENDENT SCHRÖDINGER EQUATION?
Author(s) -
ENDERS PETER
Publication year - 1996
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/(sici)1099-1204(199607)9:4<321::aid-jnm252>3.0.co;2-h
Subject(s) - matrix (chemical analysis) , diffusion equation , transmission line , line (geometry) , schrödinger equation , heat equation , transmission (telecommunications) , stability (learning theory) , mathematics , diffusion , eigenvalues and eigenvectors , separable space , yield (engineering) , mathematical analysis , physics , computer science , quantum mechanics , engineering , chemistry , telecommunications , metric (unit) , geometry , chromatography , thermodynamics , operations management , machine learning
By virtue of the success of the transmission line matrix method (TLM) in solving heat and matter diffusion problems, it should also be applicable to the time‐dependent Schrödinger equation. The occurrence of complex‐valued circuit elements does not destroy the unconditional stability of the routine. But it seems to be impossible to obtain stationary (eigen)solutions to this equation as well as separable solutions to the diffusion equation. It is suggested that this is due to the non‐dissipativity of the TLM routine.