
Laplacian Over Hyperbolic Prolate Spheroidal Coordinate, And The Integrals Of Hydrogen Molecular 

Hyperbolic Prolate Spheroidal Coordinates is called hyperbolic Confocal Elliptic Spheroidal Coordinates.
This coordinates is used for the hydrogen molecule and the hydrogen molecule ion in quantum mechanics. This site mentions about Laplacian and integrals. The integrals on the ground state energy of hydrogen molecular are overlapintegral, Coulomb integral, Exchangeintegral. The solution methods of Slater type wave function over hyperbolic Prolate Spheroidal Coordinates are Valence Bond orbital method (VB method or HL method, W. Heitler and F. London) and the simplest LCAO Molecular Orbital method (Simple LCAO MO method).
There is the important electron exchange interaction in the Hamiltonian of two electron hydrogen molecular.
Here we focus this two electron exchange interaction in hydrogen molecular.
Initially, Mulliken's approximation equation is used for <ABBA> in a simple discussion of two electron exchange interaction.
In the Bohr Model of initial quantum mechanics, 2D hyperbolic Prolate Spheroidal Coordinates is used, and the 3D Coordinates is also used for solving the electronic wave function of hydrogen molecular and hydrogen molecular ion. The Laplacian (Laplace operator) is important for solving the wave functions. In this section, the solution of Laplacian over hyperbolic Prolate Spheroidal Coordinates is mentioned.
 Hyperbolic Elliptic Cylindrical Coordinates
 Laplacian Over Hyperbolic Elliptic Cylindrical Coordinates
 Hyperbolic Prolate Spheroidal Coordinates
 Laplacian Over Hyperbolic Prolate Spheroidal Coordinates


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