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To overcome this difficult, we defined regularization of Laplacian. In particular, we computed polar coordinate expression of regularized Laplacian which can not do without regularization[2]. We try to rewrite given regularized spherical Laplacian from the point of quantum mechanics on an infinite dimensional space. We eliminate the difficulty comes from infinite dimensional property of the space, by introducing a Jordan algebra, which is non-associative. In finite dimensional case, Jordan algebra has been used to define Dirac kind operator ([5],[10]). 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