Titlebook: Wave Equations in Higher Dimensions; Shi-Hai Dong Book 2011 Springer Science+Business Media B.V. 2011 High dimension quantum theory.Higher

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Introductioned that many works along this line have been carried out in the usual three dimensional space. However, what extra dimensions could there possibly be if we never see them? It turns out that we do not really know yet how many dimensions our world has. Nevertheless, all that our current observations t

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Dirac Equation in Higher Dimensionseen contributed to the Schr?dinger equation case. On the contrary, the studies of the Dirac equation in higher dimensions are less than those of the Schr?dinger equation case except for the works in usual three-, two- and one-dimensional space. In this Chapter, we shall generalize the Dirac equation

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Special Orthogonal Group SO(,)fined by orthogonal .×. matrices, we shall give a brief review of some basic properties of group O(.) based on the monographs and textbooks. We first outline the development in order to make the reader recognize its importance in physics and then review the tensor and spinor representations of the g

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Klein-Gordon Equation in Higher Dimensions in quantum mechanics. As illustrated above, the main contributions have been made to the Schr?dinger and Dirac equations. During the past several decades, however, the Klein-Gordon equation with the Coulomb potential has been studied in three dimensions such as the operator analysis, in an intense

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Rotational Symmetry and Schr?dinger Equation in ,-Dimensional Spacehe object still looks the same, i.e., it matches itself a number of times while it is being rotated. In the language of quantum mechanics, isotropy of space means that the system Hamiltonian keeps invariant by a rotation. In our case the Schr?dinger equation with the spherically symmetric fields pos

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Harmonic Oscillator quantum mechanics. Even though the linear harmonic oscillator may represent rather non-elementary objects like a solid and a molecule, it provides a window into the most elementary structure of the physical world. In this Chapter, we shall study its exact solutions in arbitrary dimensions, the recu

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