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Quantum Mechanics

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Schrödinger structurally representing the atomic electron with the wave function (equ 63) that depicts standing waves that are used to derive the energy equation (hv) (Schrödinger, p. 1056). The atomic orbital equations are derived by representing Schrödinger's wave equation with a spherical coordinate system

-(h2/2m)∇"Ψ + U(r, θ, φ) )Ψ(r, θ, φ) = EΨ(r, θ, φ)..........................................................................64

Schrödinger's normalized wave is represented with an electron probability wave but a position probability can only represent a positive value or zero and cannot depict a negative value that is required in representing destructive wave interference used to derive the equations of the atomic orbitals. Also, Schrödinger's wave function (equ 63) represents a plane wave which conflicts with Schrödinger's wave equation (equ 64) represented with a spherical coordinates system that depicts a spherical wave that oscillation decreases with the inverse of the distance. Using Schrödinger's wave function (plane wave) (equ 63) in a spherical coordinate system is mathematically invalid since a plane wave is not a spherical wave. Proof: ++ The spherical coordinate system of Schrödinger's equation depicts a spherical wave yet none of the equations of the atomic orbitals depict a spherical wave. On top of that, the derivation of the atom's structure ends after Schrödinger's particle-in-box transformation (normalization) since the reason for the box normalization was because the de Broglie atomic electron matter wave could not be represented in a spherical coordinate system since the path of the oscillating matter wave around an atomic nucleus conflicts with the spherical coordinate system that begins at the origin an extends to the outer radius of the atom.
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