Quantum mechanics use Planck's black body derivation of the energy element (hγ) that represents the quantization of Maxwell's electromagnetic field but Planck's derivation is based on the black body surface electrons oscillating an ether that motion forms electromagnetic standing waves that are used to quantize Maxwell's electromagnetic field yet the black body radiation effect forms in vacuum that is void of an ether, composed of matter, and an expanding electromagnetic field cannot sustain the particle structure of a propagating photon. Furthermore, the quantum mechanics wave packets are used to represent a wave propagation mechanism of light using wave packets that are formed by the superpositioning (interference) of photon position probability waves but only the first and last wave packets are used to represent the propagation of light yet a series of wave packets are formed between the initial and last wave packets that represent the distance propagated. All of the photons have an equal probability to be distributed between the first and last wave packets yet the wave packet mechanism is implying that the photons are concentrated within the first and last wave packets. Furthermore, a photon probability waves that are used to construct the wave packets can only represent a positive value or zero since the photon probability depicts the possible position of a photon; consequently, a position probability cannot depict a negative value that is required in representing destructive wave interference used to construct the wave packets since the minimum value of a photon position probability is zero. Schrödinger's complex conjugate is used to represent destructive wave interference of the photon probability waves (Schrödinger, p. 1066) but the result of the complex conjugate is the cancellation of positive vectors which is mathematically invalid. 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.
The derivation of Schrödinger's photon energy equation is described. de Broglie's electron matter wave is used to represent the structure of the Bohr atom (fig 23) but the circular atomic electron matter wave contained in a circular path, around a nucleus, cannot be represented in a rectangular, cylindrical or spherical coordinate system and the electron depicted with an electron matter wave would simultaneously exist on both sides of an atom. Plus, for a multiple proton atom, positive charged protons cannot exist in the infinitesimal volume of a nucleus. Schrodinger takes Bohr's circular electron matter wave and flattens the curved axis of the oscillating electron matter wave into a straighten axis electron matter wave then replaces the electron matter wave with an electromagnetic wave that is then inserted into a hypothetical box allowing the electromagnetic wave to resonate, within a box, forming an electromagnetic standing wave without the nucleus which depicts Schrödinger transformation (normalization) of the Bohr atomic electron matter wave into a particle-in-a-box electromagnetic standing wave (fig 24) depicted with Schrödinger's wave equation using a rectangular coordinate system,
-(h2/2m)∇"Ψ( x,y,z) + V(x,y,z) + V(x,y,z)Ψ(x,y,z) = EΨ(x,y,z)...................................................81
A solution to Schrödinger's wave equation is represented with the wave function,
Ψ = Σ c u exp[(2πEt/h + θ)i]............(Schrodinger, p. 1065)......................................................82
"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 fluctuation of the charge will be governed by the Eq. 28, applied to the special case of the hydrogen atom. To find the radiation, that by electrodynamics will originate from these fluctuating charges, we have simply to calculate the rectangular components of the total electric moment by multiplying (28) by x, y, z respectively, then integrating over space, e.g." (Schrodinger, p. 1066).
"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).
Schrödinger's wave function (equ 82) is a solution to Schrodinger's normalized wave equation. The transition of Schrodinger's normalized electromagnetic standing wave, depicted with the wave function, 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) represents the units of the kinetic energy (kg m2 / s2) yet a photon is mass-less.
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A solution to Schrödinger's wave equation is the wave function (equ 82) represented with,
-(h2/2m)∇"Ψ + U(r, θ, φ) )Ψ(r, θ, φ) = EΨ(r, θ, φ)..........................................................................83
The normalization of the Bohr's atomic matter wave depicted with Schrodinger's wave equation (equ 81) eliminates the atomic nucleus and replaces the structure of an atom with a hypothetical box; consequently, the derivation of the atomic structure ends with the box normalization yet Schrödinger’s wave equation is represented with a spherical coordinate system (equ 83) in the derivation of the equations of the atomic orbital but Schrödinger’s wave function depicts a resonating electromagnetic wave that is representing an electron encircling a nucleus that is transformed into the box normalization rectangular coordinate system that is incompatible with a spherical coordinate system that begins at the origin since a Bohr’s atom matter wave does not have an origin. Also, Schrodinger normalization eliminates the nuclear protons yet a multiple proton element has a neutral charge which cannot be obtain without the nuclear protons which proves the derivation of the equation of the atomic orbitals is physically invalid.
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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)......................................................................................84
E(r,t) = - ∇ɸ(r,t) - d/dtA(r,t).......................................................................85
....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 quantum mechanics gauge transformation 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 is not luminous nor can the potential of a mass-less and expanding electromagnetic field be used to represent the particle structure of an electron, proton, neutron or atom that has a mass.