(Fig.1) ↓ Schrödinger's wavefunction = classical orbit
Schrödinger equation of quantum mechanics gives exactly the same energy levels and electron's orbital radius as classical orbit in hydrogen.
Quantum mechanics also uses de Broglie wavelength, which determines the average electron's orbital radius.
The average electron's orbital radius in ground state hydrogen agrees with Bohr radius (= a ) in both quantum mechanics and classical orbit.
So even the lowest-energy electron keeps some distance (= a ) from the nucleus, as far as the orbit is an integer times de Broglie wavelength (= boundary condition in quantum mechanics ).
(Fig.2) ↓ Unreal quantum wavefunction = an electron everywhere !?
Due to de Broglie wavelenth, an electron keeps some distance from the nucleus in both quantum wavefunction and classical orbit even in the ground state.
When two hydrogen atoms form hydrogen molecule, the lowest energy state is when two electrons just avoid each other as shown in Fig.2 upper.
In classical orbit, we can easily find this lowest energy state in any molecules.
For example, In methane (= CH4 ), the tetrahedral distribution of carbon's four valence electrons is the lowest energy (= electrons avoid each other ), which can be easily found.
The problem is quantum mechanical wavefunction gives vague electron cloud spreading over all space, which means each electron is always everywhere.
If an electron is vague electron cloud, electrons cannot avoid each other in quantum mechanics !
When an electron of one atom approaches another nuclei and another electron moves away to the opposite side, it is the lowest energy state (= Fig.2 upper ).
But quantum wavefunction must always spreads over all space (= electron's probability is Not zero in any points ), which always includes higher-energy electron's positions.
It means classical orbits can easily find the lowest-energy electrons' positions (= useful !), while quantum mechanics must take infinite time to find the lowest-energy fake solution from infinite choices (= useless, impractical ).
See this p.12, this p.19
(Fig.2a) ↓ Calculating two charges is impossible in ?
The current basic science is impractical, biologists and chemists ignore quantum mechanics due to useless Schrödinger equation ( this p.1 left ).
In classical physics, calculating force between two charges is very easy, but quantum mechanics can hardly calculate even this simple force !
Quantum mechanics treats each electron as vague cloud spreading over all space, which makes calculating electrons' force impractical in quantum mechanics.
If a single electron is spreading over space like quantum mechanics, electrons cannot avoid each other, which is unreal.
We have to calculate almost infinite patterns of Coulomb energies between small charges inside two electrons' clouds, and sum them up, which takes enormous time ( this p.4, this p.8 ).
On the other hand, in classical electron = point charge, we just do only one calculation of Coulomb force between two electrons, which is much easier, and takes almost no time.
Why must a quantum mechanical electron always spread in all space ? Because Schrödinger equation cannot distinguish between electron particle and de Broglie wave (= field ).
In quantum mechanics, de Broglie relation is expressed as derivative, which becomes infinity when an electron is a point charge = delta function.
But actual electrons are moving particles avoiding each other !
Effective nuclear charge which a helium electron feels is 1.69, bigger than 1, which means two electrons in helium are always avoiding each other ( this p.3, this last ).
And spreading electron clouds in quantum mechanics make it impossible to conserve total energy in multi-electron atoms, so wrong.
(Fig.2b) ↓ Electron's kinetic energy = derivative of wavefunction.
The most crucial difference between quantum mechanics and realistic Bohr model is the definition of a particle and wave.
Quantum mechanics dismissed real entities such as an electron particle and de Broglie wave, instead, it just mixes a partcle and wave as one nonphysical wave function.
Therefore, in quantum mechanics, even a single electron spreads out over all space as fuzzy electron cloud (= whether an electron is a particle or wave is uncertain ).
They claim this fuzzy cloud densities at different areas show "different probabilities" of finding an electron. ← This forced interpretation has No factual grounding.
If quantum mechanical picture is correct, a single particle has to pass through two slits at once like a ghost using fantasy parallel worlds to cause observed interference.
In Bohr's realistic picture, an electron just passes through one of two slits, and de Broglie wave around the electron can pass both slits, which model can naturally explain two-slit interference without relying on fictional quantum parallel worlds.
These quantum electron clouds cannot avoid other electrons, so to get molecular binding energy, quantum mechanics has to rely on "cheating" to lower total energy in unfair way which lowers only kinetic energy by violating energy conservation law and Virial theorem ( this p.3 ).
So quantum mechanical molecular bonds based on cheating have nothing to do with actual molecules, hence physically meaningless. ← Another proof that quantum mechanics is wrong.
Quantum mechanical wavefunctions interpreted as "electron's probability" cannot avoid each other, because the electron cloud wavefunction must be always symmetrically distributed around the nucleus (= hence, the electron's probability also must be evenly distributed around the nucleus ).
If we try to localize each electron to one side of a nucleus to avoid another electron, quantum "electron-probability" wavefunction needs to be sharper at the electron's point, therefore drastically increasing the electron's kinetic energy which is expressed as a derivative of wavefunction.
For example, if we try to express quantum electron as a localized point particle like classical atomic model, the electron's probability wavefunction needs to be sharp delta function at the electron's position where the electron's kinetic energy (= derivative of wavefunction or delta function ) increases to infinity, which cannot form stable molecular bond (= lowering total energy is impossible ).
So the only realistic molecular model obeying energy conservation law by electrons avoiding each other must be like Bohr model where each electron is an actually moving particle and its de Broglie wave is generated around the electron particle (= so separating a particle from its wave is necessary. )
In this realistic Bohr model where an electron particle is separated from de Broglie wave generated around an electron particle, de Broglie wave has nothing to do with the electron's probability wavefunction, hence, an electron particle can be localized in one particular place without sharpening electron's probability wavefunction (= sharper wavefunction means shorter de Broglie wavelength and increasing electron's kinetic energy in unphysical quantum mechanics ) or increasing kinetic energy.
Mixing a electron particle and wave as "one weird probability wavefunction" as seen in quantum mechanical Schrödinger equation is unable to describe actual stable molecules.
(Fig.3) ↓ Classical orbit vs. useless quantum molecule = No force.
In classical orbit, electrons are point particles separated from each other, so it can easily find the most stable (= the lowest energy ) electrons' position.
The lowest-energy state is when electrons just avoid each other between and inside atoms.
After finding the lowest-energy state, we can easily calculate force between atoms, and predict which direction each atom will move in new chemical reaction.
Quantum mechanical wavefunction is vague electron cloud, which cannot avoid each other, so it's very hard (= impossible ! ) to find the lowest-energy molecular wavefunction.
If a single electron is Not a point particle but spreading over all space as cloud, two electrons don't feel repulsion from each other, when they are outside of each other, as seen in spherical charge.
Only when two wavefunctions penetrate each other (= inside spherical electron charge ), it feels more attraction from another nucleus, causing molecular bond ?
Quantum mechanics needs infinite time to find the lowest-energy wavefunction from infinite choices, artificially changing trial wavefunctions and the amount of electron penetration.
Quantum mechanics cannot calculate "force", which makes itself useless, because "energy" does not tell us "direction" in which atoms will move in chemical direction.
Estimating force is much easier, because we only consider a few electrons between atoms, while when computing energy, we have to consider the "whole orbital" (= all other many electrons involved ).
The worst point of quantum mechanics is its molecule cannot satisfy energy conservation ( an electron penetrating another electron is lower energy than outside ).
(Fig.4) ↓ Overlapped part is lower energy = No energy conservation !
The problem is Schrödinger's atoms cannot satisfy energy conservation law, so unreal.
Even when two hydrogen atoms overlap, each hydrogen's electron energy is conserved only with respect to each nucleus, Not to another nucleus.
A part of electron cloud penetrating another electron cloud feels more attraction , this overlapped wavefunction part (= feels both nuclei ) is lower energy than outside of cloud (= feels only one nucleus ), so total energy is Not conserved in different positions.
When wavefunction is antisymemtric (= when exchanging r1 and r2, it becomes minus ), it causes Pauli exclusion principle, they insist.
In Fig.4 lower (= antisymemtric, Pauli ), overlapped part (= lower energy ) is cancelled, leaving only higher energy part, so the total is higher energy, which causes Pauli repulsion force ?
This Pauli principle by quantum mechanics depends on unreal condition (= energy is Not conserved between overlapped and non-overlapped parts ), so untrue.
(Fig.5) ↓ Antisymmetric wavefunction = Pauli repulsion ?
Quantum mechanic uses two hydrogen atoms (= 1s wavefunction φ ) around different nuclei as hydrogen molecule (= H2, this p.3 ).
Overlapped part of two wavefunctions feels stronger attraction from another nucleus, which causes molecular bond energy in quantum mechanics.
When the entire wavefunction is antisymmetric, this overlapped part is cancelled ( minus - in Fig.5 ), which causes Pauli repulsion, they claim.
If this Pauli exclusion principle is correct, total energy is Not conserved inside molecular wavefunction.
Triplet energy is lower than singlet ? uses the same trick (= overlapped part is higher than other parts due to electron-electron repulsion ), so wrong.
This quantum mechanical triplet-singlet methods give wrong results.
Quantum mechanics = 1s2p-anti is lower than 1s2s-sim ( this last ), different from 1s2s is lower in experiments
Schrödinger equation cannot have exact solution in any multi-electron atoms, so they just choose convenient wavefunction as fake solution. ← meangingless.
(Fig.6) ↓ H2 molecule wavefunction, symemtric (+) and anti (-).
Suppose H2 molecule consists of two hydrogen atoms (= φa, φb ).
When exchanging r1 and r, one wavefunction remains the same, another antisymemtric wavefunction becomes minus (= Pauli exclusion ? ).
Schrödinger equation of H2 molecule cannot be solved, all they can do is integrate wavefunctions to get approximate energy E instead of solving it ( this p.9 ).
It gives two energies of total (= the first term ) and overlapped (= the second term ) part wavefunction, as shown in Fig.6 lower.
When these two energies are different (= violating energy conservation. so unreal ), it causes molecular bond or Pauli exclusion (= unreal, too )
(Fig.7) ↓ Electron in overlapped part is lower-energy than outside ?
For Pauli principle by quantum mechanics to be effective, electron in overlapped and non-overlapped parts needs to be in different energy states.
Whether wavefunction is symmetric (= + ) or antisymmetric is irrelevant. Because after normalize it, this difference is canceled out, and both probabilities (= integral ) become "1".
1/1±S is normalization coefficient.
So when total energy is normally conserved (= energies of ① and ② are the same E ), the total energy is always E, which doesn't cause Pauli exclusion force or molecular bond.
When the average energy (= ② ) of overlapped part is lower than the average total energy (= ① ), the average total energy (= E± ) of ① ± ② becomes lower (= E+ = molecular bond ) or higher (= E- = Pauli ).
So as long as the total energy E is conserved in any positions of molecular wavefunction, Pauli exclusion force by antisymmetric wavefunction is meaningless, and does Not occur.
(Fig.8) ↓ Energy is conserved = E± = E. ← No Pauli
When Schrödinger equation has solution, it means total energy E is always conserved in any position of solution wavefunction.
Symmetric and antisymmetric wavefunctions give the same energy E, when the energy is conserved.
Because the first term and the second term of ther upper wavefunction have the same form, just exchanging variables r1 and r2.
And energy equation (= H ) is unchanged, when exchanging 1 and 2, which gives the same total energy E in both terms. ← quantum Pauli principle is invalid.
So only when the total energy E is Not conserved, which means antisymmetric wavefunction causing Pauli principle is Not exact solution, quantum Pauli principle emerges. ← paradox !
As a result, Pauli principle by unreal spin is false and unreal.
We multiply wavefunction by normalization coefficient, both the squares of anti- and symmetric wavefunctions (= probability ) become 1, so the difference of ± is gone. = the same total energy E by integral.
(Fig.9) ↓ Total energy is Not conserved in different area → Pauli principle ?
We explain why quantum mechanical Pauli principle is wrong.
Pauli exclusion principle says two electrons cannot occupy the same orbital, which is why the 3rd electron of lithium cannot enter 1s orbital.
The force of this Pauli exclusion is mystery, as strong as Coulomb force, but Not fundamental force ?
Electron spin lacks reality, its spinning speed is superluminal. Electrons spin is too weak to cause Pauli exclusion force.
They say this Pauli exclusion force is caused by "antisymmetric wavefunction", where the sign of total wavefunction becomes the opposite, when exchanging variables of two functions.
So when two electrons are in the same orbital, the total wavefunction becomes zero, which nonphysical concept really causes Pauli principle ?
This Pauli principle by quantum mechanics is just wrong.
The square of wavefunction (= electron probability ) must be always 1, so the total wavefunction cannot be zero (= quantum Pauli is invalid ), because we have to get it back to 1 by multiplying it by the normalization constant.
In fact, quantum Pauli principle needs violation of energy conservation !
They use H2 molecule consisting of two H atoms. In this case, there is energy difference between symmetric and antisymmetric wavefunctions, which violates energy conservation.
Only inside each H atom, the total energy is conserved independently from another electron, because they use H atom wavefunction, which can be solved.
It means the total energy of the whole H2 molecule is Not conserved, where the overlapped part (= close to both nuclei ) is in lower energy than nonoverlapped part.
So antisymmetric wavefunction which cancels overlapped part gives higher total energy, which Pauli exclusion force is caused by violation of energy conservation, so unreal.
If the total energy of molecule is conserved, both overlapped and non-overlapped parts must give the same total energy, invalidating quantum mechanical Pauli principle.
Just exchanging variables (= 1 and 2 ) in molecule doesn't change its total energy, so there must Not be energy difference between symmetric and antisymmetric wavefunctions, if they are exact solutions (= conserve total energy ).
Schrödinger equation has No exact solution except H atom. They just choose fake solution from infinite choices (= infinite time is needed ! ) and integrate it instead of solving it, which cannot predict anything.
In 1920s without computer, physicists couldn't compute complicated integral. All they could do was express molecule mixing simple H atom orbitals.
In pi bond, H atomic s and p orbital is canceled ? 1s and 2s H atom wavefunctions cancel each other, invalidating antisymmetric Pauli principle ( this p.2 ) ? These artificial models rely on empirical parameters.
All these rough approximations violate total energy conservation of molecules, they use this violation as quantum Pauli principle, which is unreal.
Experimental proof of de Broglie wave interference and radiation pressure indicates some "medium pressure" causes real Pauli exclusion force.
(Fig.10) ↓ Total energy is Not conserved in H2 molecule. → bond energy ?
An electron of Schrödinger equation must always spread over all space as electron cloud, so electrons cannot avoid each other in quantum mechanical molecules.
It means quantum mechanical molecules always give higher energy than real molecules (= electrons of real molecules can avoid other electrons ). Then, how do those quantum molecules form stable bonds between atoms ?
In fact, quantum mechanics relies on "cheating" in molecular bonds.
They say H2 molecule approximately consists of two H atomic 1s wavefunctions.
In each H atom, the total energy (= kinetic + Coulomb potential energy ) is constant, conserved in any electron's positions.
When an electron approaches H atom nucleus, Coulomb potential energy is lower, its kinetic energy becomes higher, therefore the total energy is unchanged = conserved constant.
But when they use this H atom wavefunction as a part of H2 molecule, the total energy is Not conserved. ← quantum mechanical molecule is wrong.
Because even when an electron approaches another H atom nucleus (= Coulomb potential energy decreases ) in H2 molecule, its kinetic energy still keeps decreasing, so the total energy keeps decreasing, violating energy conservation law.
The total energy of each electron is seemingly conserved only around the area near either of two nuclei closer to the electron.
But each hydrogen wavefunction spreading over all space can reach another distant nucleus, decreasing both its kinetic energy and Coulomb potential energy.
As a result, the total energy = kinetic energy + Coulomb potential energies is Not conserved or constant in quantum mechanical molecule.
Quantum mechanical molecule uses this violation of energy conservation (= decreasing kinetic energy in an unfair way ) as fake binding energy, which is nonsense and unreal.
Each H atomic 1s wavefunction includes only one crest, where steep slope means higher kinetic energy, gentle slope is lower kinetic energy.
For the total energy to be conserved also in H2 molecule, the basic wavefunction must consists of at least two crests.
Quantum mechanics is "cheating" to form molecules, so false.
(Fig.11) ↓ Dirty trick in hydrogen molecules H2.
Quantum mechanics says hydrogen molecule (= H2 ) approximately consists of two Hydrogen 1s wavefunctions.
Each Hydrogen 1s wavefunction belongs to either nucleus of H2 molecule in each term (= In the different term, two electrons are swapped, the total energy remains the same, so we think only about one term ).
For example, in the first term of ψ+ wavefuncton of Fig.11, the electron 1 (= r1 ) belongs only to Hydrogen-1 nucleus (= φa ).
Coulomb attractive potential energy of Hydrogen molecule includes ones between each electron and both of two Hydrogen nuclei-1 and 2.
Coulomb attractive potential energy of the electron-1 consists of two terms ( -e2/ra1 and -e2/rb1 ) from both two nuclei.
So as electron 1 is farther away from Hydrogen-1 nucleus, its Coulomb potential energy becomes higher (= -e2/ra1 is higher ) and its kinetic energy becomes lower to cancel the increasing potential energy to conserve total energy E.
But as as electron 1 is farther away from Hydrogen-1 nucleus, the electron is closer to Hydrogen-2 nucleus and its Coulomb potential energy becomes lower (= -e2/rb1 is lower ), but its kinetic energy remains lower, too.
This means violation of conservation of total energy.
Because as the electron's potential energy is lower, its kinetic energy also becomes lower.
This is a dirty, wrong math trick for quantum mechanics to lower the total energy of molecules in a wrong way.
So quantum mechanics is false, and its wavefunction lacks physical reality.
(Fig.12) ↓ Overlap integral exacerbates violation of energy conservation.
In calculating Schrödinger equation of hydrogen (H2) molecule, we often pick up two hydrogen 1s atoms's wavefunctions (= φa and φb ) as approximate (= fake ) H2 molecule solution.
To seemingly get molecular bond energy by lowering total energy in quantum mechanical illegitimate "cheating", they use symmetric wavefunction where exchanging two electrons' variable numbers (= r1 and r2 ) gives the same original form of wavefunction (= this is just an artificial rule ).
An electron-1 (=r1) shares two hydrogen atomic wavefunctions φa(r1) and φb(r1).
An electron-2 (=r2) also shares two hyrogen atomic wavefunctions φa(r2) and φb(r2). See this p.3
By integrating this fake H2 solution with Hamiltonian H (= total energy ), we obtain overlap (or exchange ) integral ( this p.14, this last ).
As I said, quantum mechanical molecule has to rely on "cheating" to lower total energy and get some molecular bond energy.
Kinetic energy of Hamiltonian H acts on hydrogen atom φa(r1) in Fig.12. This electron-1 kinetic energy keeps decreasing even when the electron-1 approaches another H2 atomic nucleus and lowers potential energy.
Because this electron-1 is supposed to conserve total energy only around H1 atomic nucleus. As the electron-1 gets farther away from H1 atomic nucleus (= approaching another H2 atomic nucleus ), its kinetic energy decreases offsetting higher potential energy between electron-1 and H1 atomic nucleus.
The energy change between electron-1 and another H2 atomic nucleus clearly violates total energy conservation, because both kinetic and potential energies decrease when the electron-1 approaches another H2 atomic nucleus.
Overlap (= exchange ) integral enhances this illegitimately lowered kinetic energy by multiplying φa by φb (= this amplitude is higher around H2 atomic nucleus ).
Lowering kinetic energy (= enhanced by overlap integral in symmetric wavefunction ) by violating total energy conservation and Virial theorem is the origin (= cheating ) of quantum mechanical molecular bonds.
This "cheating" shows quantum mechanical wavefunction is unable to form molecular bonds in the right and legitimate way, so quantum mechanics is false.
2020/3/11 updated. Feel free to link to this site.