CALCULATION OF THE ENERGY OF ONE-AND TWO-ELECTRON ATOMS IN SPACES OF THREE OR FEWER DIMENSIONS

skobelev skobelev

Abstract


Abstract:  The well-known variation method of calculating the total energy of a two-electron atom is generalized to the case of any set of quantum numbers of electrons in spaces of three or fewer dimensions, yielding the corresponding expressions for energy and screening constant. From these results, the particular cases of the basic and the lowest excited states follow, as earlier considered by us and other authors. We clarify the correct use of these results. Moreover, we generalize the standard relations connecting the average values of kinetic and potential energy with the total energy of an electron in a nucleus field in three dimension for any quantum state and extend it to subspaces of one and  two dimensions in a three-dimensional space. The results of this work could be a useful addition to a university course on quantum mechanics.

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