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The generalized Schr\\\"odinger equation","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dominic Rochon, S\\'ebastien Tremblay","submitted_at":"2007-09-20T14:27:05Z","abstract_excerpt":"We introduce the set of bicomplex numbers $\\mathbb{T}$ which is a commutative ring with zero divisors defined by $\\mathbb{T}=\\{w_0+w_1 \\bold{i_1}+w_2\\bold{i_2}+w_3 \\bold{j}| w_0,w_1,w_2,w_3 \\in \\mathbb{R}\\}$ where $\\bold{i^{\\text 2}_1}=-1, \\bold{i^{\\text 2}_2}=-1, \\bold{j}^2=1,\\ \\bold{i_1}\\bold{i_2}=\\bold{j}=\\bold{i_2}\\bold{i_1}$. We present the conjugates and the moduli associated with the bicomplex numbers. Then we study the bicomplex Schr\\\"odinger equation and found the continuity equations. 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