Eigenfunctions spheroconal coordinates

Niven established the connections between the ellipsoidal harmonics, expressed in cartesian coordinates, and the spheroconal harmonics, expressed in spheroconal coordinates, in the respective factors of Eq. (18), by requiring that the eigenfunctions h satisfy the Laplace equation [18]. The application of the Laplace operator on the eigenfunctions with the condition of vanishing leads to the zeros 0, of the respective polynomials, which are real and different in their respective domains ccartesian coordinates leads to the corresponding condition for its being harmonic... 

The chapter contains a review of the free hydrogen atom eigenfunctions in the spherical, spheroconal, parabolic, and prolate spheroidal coordinates an overview of our own works for confinement by most of the above-mentioned boundaries and a preview of problems on confined atoms and molecules of current and future investigations. 

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