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de Broglie electron matter wave is used to represent an atomic electron (fig 8) but the electron matter wave does not function in the three dimensional representation of a spherical shape atom that represents a volume. Using a 8 cm ring, that is at the equator of the sphere and four pairs of parallel rings that have a diameters of 4 cm and 2 cm and two small spheres at the top and bottom of the sphere where the rings and small spheres represent the positive and negative field structure of the electron matter wave that is used to represent the structure of the atom. The electron matter wave would form around the circumference of a spherical shape atom but in the direction parallel to the rings, a constant amplitude or zero is formed and a electron matter wave oscillation would not be produced; consequently, the electron atomic matter wave only function in the two dimensional representation and does not function in the three dimension structure of an atom. In addition, the atomic electron matter wave cannot be represented in a cartesian, cylindrical or spherical coordinates system; consequently, the physically invalid atomic electron matter wave is transformed into a particle-in-a-box (fig 9) and represented in a rectangular coordinate system (x,y,z),

-(h2/2u)∇"Ψ(x,y,z) + V(x,y,z) + V(x,y,z)Ψ(x,y,z) = EΨ(x,y,z)..................64

The electron matter does not function in the three dimensional representation of an atom which proves that the particle-in-the box representation is physically invalid. To form the particle-in-box transformation requires that the original electron atomic matter wave function which clearly does not; consequently, the validity of the quantum mechanic derivation of the atomic orbital equations, based on the electron matter wave, is physically invalid and ends here, at the box normalization level.

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Schrödinger transforms the particle-in-a-box electron matter wave, of equation 64, into a probability wave, that is represented in spherical coordinate system (r,Θ,φ,),

-(h2/2u)∇"Ψ(r,Θ,φ) + V(r,Θ,φ) + V(r,Θ,φ)Ψ(r,Θ,φ) = EΨ(r,Θ,φ)..................65

"As an alternative, in 1926 German physicist Max Born sharply refined Schrodinger's interpretation of an electron wave, and it is his interpretation--amplified by Bohr and his colleagues--that is still with us today......He asserted that an electron wave must be interpreted from the standpoint of probability." (Greene, p. 105).

"Just a few months after de Broglie's suggestion, Schrodinger took the decisive step toward this end by determining an equation that governs the shape and the evolution of probability waves, or as they came to be known, wave functions." (Greene, p. 107).

"Schrodinger, de Broglie, and Born explained this phenomenon by associating a probability wave to each electron." (Greene, p. 109).

Schrodinger's wave equation (equ 65) originates from the atomic electron matter wave that does not function in the three dimensional representation of an atom and the atomic electron wave could not be represented in a spherical coordinate system yet Schrodinger is representing the atomic electron wave with a probability wave, in a spherical coordinate system but the electron probability, in a spherical coordinate system, represents the variable (r) that originates from the center of the atom to the outer circumference of the atom which conflicts with the original atomic electron matter wave that exist only at the outer circumference of the atom and does not exist near the origin yet Schrodinger's electron probability exist at the origin and in the volume between the origin and the outer radius which proves the derivation of the atomic orbital equations is based on a deceptive mathematical manipulation.