• #### Quantum Mechanics

From carl eto@21:1/5 to All on Fri May 5 12:51:03 2023
Quantum Mechanics

Quantum mechanics is based on Planck's quantization of Maxwell's electromagnetic wave (Planck, Intro) but an expanding electromagnetic field cannot form a particle structure. Davisson–Gerber (1927) electron diffraction experiment is used to justify
wave interference using interfering electron matter waves but the destruction of electrons, using electron wave interference, to form the non-electron fringes of the electron diffraction pattern represents the arbitrary destruction of electrons.

In "An Undulatory Theory of the Mechanics of Atoms and Molecules" (1926), Schrödinger's photon energy equation is derived. First, de Broglie's electron matter wave is used to represent the structure of the Bohr atom but the atomic electron matter wave
oscillating along the outer circumference of the Bohr atom (fig 1) cannot be represented in a rectangular, cylindrical or spherical coordinate system; consequently, Schrodinger replaces Bohr's circular atomic electron matter wave with a linear
electromagnetic wave that is resonating within a hypothetical box (fig 2) that is depicted with Schrödinger's wave equation.

-(h2/2m)[∇2 Ψ( x,y,z)] + V(x,y,z) + V(x,y,z)Ψ(x,y,z) = EΨ(x,y,z)...................................................1

A solution to Schrödinger's wave equation (equ 1) is represented with the wave function,

Ψ = Σ c u exp[(2πEt/h + θ)i]............(Schrodinger, p. 1065)........................................................2

"The wave-function physical means and determines a continuous distribution of electricity in space, the fluctuations of which determine the radiation by laws of ordinary electrodynamics." (Schrödinger, Abstract).

"the frequency v will be given by v= E/h....................(11) , h being Planck's constant. Thus the well known universal relation between energy and frequency is arrived at in a rather simple and unforced" (Schrödinger, p. 1056).

The transition of Schrodinger's normalized electromagnetic standing wave to a lower energy level results in the emission of a photon that energy is represented with Schrodinger's photon energy equation (hv) (Schrödinger, p. 1056) but Schrodinger's
photon energy equation (hv) is represented with the units of the kinetic energy (erg = g m2 / s2) yet a photon is massless.

"(#15) h = 6.55 . 10-27 erg . sec" (Planck, § 12).

……………………………………………………………………………………………………………………

The derivation of the equations of the atomic orbitals is described using Schrödinger's wave equation in a spherical coordinate system using the Laplacian operator,

-(h2/2m)∇2 Ψ + U(r, θ, φ) )Ψ(r, θ, φ) = EΨ(r, θ, φ)......................................................................3

The atomic orbitals do not include a nucleus since Schrodinger's box normalization eliminates the nucleus and replaces the atomic nucleus with a box. Also, the plane wave equation of Schrodinger’s wave function (equ 2) is depicted in a spherical
coordinate system using Lagrangian’s spherical coordinate system operator but the box normalized plane wave equations of Schrodinger’s wave function is patently incompatible with a spherical coordinate system which proves the atomic orbitals are
invalid.

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The negatively charged electrons of the atomic orbitals produce repulsive forces which would prevent the existence of electrons within the volume of an atom (d = 10-10 m). The electrons of the atomic orbitals of two electron hydrogen gas molecule would
form a repulsive force of:

F = k(q1 q2)/r2 = [(9 x 109) (1.6 x 10-19)2] / (2 x 10-10)2 = 6.8 x 10-10 N…………………………………4

Using Avogadro's number, a litter of hydrogen gas would form a force of,

(1 L) x (6 x 1023 molc./L) x (6.8 x 10-10 N/molc.) = 4.1 x 1014 N (185,973 megatons)………………..5

One milliliter of hydrogen gases’ negatively charged electrons, represented with the atomic orbital structure produces a total repulsive force of 186 megatons.

………………………………………………………………………………………………………………………..

Quantum mechanics uses a gauge transformation of Maxwell's equations.

"A similar, but more subtle and deep, situation arises in electrodynamics where one can express the (physical) electric and magnetic fields in terms of scalar (ɸ(r,t)) and vector (A(r,t)) potentials via

B(r,t) = ∇ x A(r,t)......................................................................................6

E(r,t) = - ∇ɸ(r,t) - d/dtA(r,t).......................................................................7

....Such a change in potentials is called a gauge transformation, and will be seen to play and important role in the quantum mechanical treatment of charged particle interactions." (Robinett, p.447); (Cohen-Tannoudji, p. 315).

The gauge is based on Maxwell's equations but the gauge potential does not change the fact that Maxwell's equations are derived using Faraday's induction effect that massless and expanding electromagnetic field cannot be used to represent the particle
structure of an electron that has a mass.

Cohen-Tannoudji, Claude., Diu, Bernard., Laloe, Frank. Quantum Mechanics. Vol. I. Wiley. 1977.

Planck, Max. On the Law of Distribution of Energy in the Normal Spectrum. Annalen der Physik. 4:553. 1901.

Robinett, Richard. Quantum Mechanics. Oxford University Press. 1997.

Schrodinger, Erwin. An Undulatory Theory of the Mechanics of Atoms and Molecules. Physical Review. Vol 28, No. 6. 1926.

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• From carl eto@21:1/5 to All on Fri May 5 15:26:22 2023
On Friday, May 5, 2023 at 12:51.
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• From carl eto@21:1/5 to carl eto on Sat May 6 11:33:41 2023
On Friday, May 5, 2023 at 3:26:24 PM UTC-7, carl eto wrote:
On Friday, May 5, 2023 at 12:51.
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