*(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 ).

*(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 can**not** 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*" can**not** 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 can**not** 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 r_{1} and r_{2}, 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 (= φ_{a}, φ_{b} ).

When exchanging r_{1} and r_{}, one wavefunction remains the same, another antisymemtric wavefunction becomes minus (= Pauli exclusion ? ).

Schrödinger equation of H2 molecule can**not** 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 r_{1} and r_{2}.

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 **non**physical 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 can**not** 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 (= r_{1} ) belongs **only** to Hydrogen-1 nucleus (= φ_{a} ).

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 ( -e^{2}/r_{a1} and -e^{2}/r_{b1} ) from both two nuclei.

So as electron 1 is farther away from Hydrogen-1 nucleus, its Coulomb potential energy becomes higher (= -e^{2}/r_{a1} 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 (= -e^{2}/r_{b1} 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 (= φ_{a} and φ_{b} ) 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 (= r_{1} and r_{2} ) gives the same original form of wavefunction (= this is just an artificial rule ).

An electron-1 (=r_{1}) **shares** two hydrogen atomic wavefunctions φ_{a}(r_{1}) and φ_{b}(r_{1}).

An electron-2 (=r_{2}) also shares two hyrogen atomic wavefunctions φ_{a}(r_{2}) and φ_{b}(r_{2}). 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 φ_{a}(r_{1}) 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 φ_{a} by φ_{b} (= 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.