Schrödinger equation  is false.

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Schrödinger's atom = parallel worlds !?

[ An electron is everywhere at the same time in quantum world ? ]

(Fig.1)  Schrödinger's hydrogen = an electron everywhere !?

Quantum mechanics uses Schrödinger equation, where a single electron can be everywhere at the same time in parallel worlds.

Quantum mechanics tries to apply these unreal parallel worlds to all atoms !

But this "parallel-world" nature of Schrödinger equation does Not work in multi-electron atoms.

Here we prove quantum mechanics is wrong.

 

No electron  in quantum mechanics ?

[ There is No clear electron, No motion in Schrödinger atom ! ]

(Fig.2)  Just vague electron cloud in quantum atom ↓

Quantum mehanics can not descibe real electrons.
It gives only vague electron cloud spreading over all space to infinity.

Strangely, though Schrödinger equation has kinetic energy, its electron is Not moving "realistically" !

This unphysical nature of quantum mechanics = "No clear electron, No electron's motion" causes serious problem in multi- electron atoms.

Because it's unreal.

 

Electron "everywhere"  in quantum mechanics !

[ Schrödinger wavefunction spreads all space ← electron everywhere !? ]

(Fig.3)  ↓ Only one-electron hydrogen has solution in quantum mechanics.

Only one-electron hydrogen atom has solution in Schrödinger equation.

Hydrogen wavefunction spreads all space, so in all space, the electron's total energy must be conserved at constant E.

Coulomb energy term must be cancelled out by kinetic energy to give constant total energy in all space.

This is impossible in multi-electron Schrödinger atoms.

 

Helium has No solution.

[ Schrödinger wavefunction is useless in Helium atom. ]

(Fig.4)   Two hydrogen wavefunctions → Helium ?

In multi-electron atoms such as Helium, Schrödinger equation cannot be solved, so useless.

Approximately, Schrödinger Helium is expressed as two hydrogen atoms, but this is Not true solution but fake solution.

If there was solution in Schrödinger Helium, two electrons of helium must spread all space, like hydrogen wavefunction.

But this "spreading" wavefunction causes serious problem in Helium.

 

Schrödinger Helium is wrong.

[ Two "independent" electrons in He → unreal H atoms !? ]

(Fig.5)  ↓ Three Coulomb terms can be changed independently !?

If Schrödinger equation had exact Helium solution, its Helium approximately consists of two hydrogen atoms ( this p.2 )

The problem is Schrödinger wavefunction always spread over all space, which causes serious problem in Helium.

We can move only electron 2 (= e2 ), so that the distances between nucleus and each electron (= r1, r2 ) are the same, and only the distance between two electrons (= |r1-r2|) changes in Schrödinger Helium, because its two electrons' motion are independent from each other.

Total energy E must be always conserved at constant E, so in this case, we must cancel only one changing Coulomb energy term (= 1/|r1-r2| ) by its corresponding kinetic energy.

In this way, in Schrödinger Helium, each Coulomb energy term can be changed independently, so it must be cancelled by its corresponding kinetic energy independently !

This is imposssible, so Schrödinger Helium is false.

 

Helium splits into three "unreal" hydrogens ?

[ Schrödinger Helium must split into three unreal hydrogens. ]

(Fig.6)  ↓ Helium = three unreal hydrogens ? ← Schrödinger is wrong !

Schrödinger wavefunction always spreads over all space, and each electron's position can be changed independently, because there is No correlation between two electrons' motions in Schrödinger Helium.

So each Coulomb energy term can be changed independently from other Coulomb terms.  ← unreal atom !

It means if Schrödinger Helium has solution, it must split into three independent hydrogen solutions ( ①, ②, ③ in Fig.6 ).

But the above ③ Coulomb term between two electrons is unreal hydrogen, because "electron-electron" hydrogen doesn't exist,  only electron-proton hydrogen exists

Furthermore, if we can divide Coulomb terms into a single term independently, it cannot express the whole property of multi-electron atom.

Because, for example, Coulomb energy between two electrons must be different and specific to different atoms (= nuclei ), so we cannot separate or treat three Coulomb terms independently !

If we can separate each Coulomb term independently, it has No relation with other Coulomb term, and cannot express the whole property specific to different multi-electron atoms.

 

Schrödinger Helium doesn't exist.

[ Two electrons must move "dependent" on another electron. ]

(Fig.7)  Each electron independent → Coulomb term independent → unreal atom

For Helium to be real, two electrons must move with time, dependently on another electron, which prevents each Coulomb energy term from changing independently.

If two electrons can move independently, each Coulomb energy term must be independent, which splits Helium into unreal three hydrogens, which doesn't exist.

This is the reason Schrödinger equation is wrong in multi-electron atoms such as Helium, and only classical orbits can give real Helium model.

But in old 1920s, there were No computers, so they couldn't handle three-body Helium electrons' motion classically, which is the reason only wrong Schrödinger equation survived.

 

Real atomic model.   → many molecules !

[ Only Coulomb relation and de Broglie wave are enough. ]

(Fig.8)   Simple model describing real atomic force is necessary.

We need only two conditions to describe all realistic molecular behavior.

If there is only Coulomb relation condition, atomic (elecron orbital) radius is not determined.

de Broglie wavelength determines atomic size, and it can explain the different sizes between carbon and silicon.

These two conditions can explain the maximum electrons' number (= Pauli principle ) correctly, without unreal spin.

This simple atomic model (= only Coulomb + de Broglie ) can be easily applied to much bigger, complicated molecules with the help of computer to cure fatal disease.

 

Quantum mechanics is useless, forever.

[ Schrödinger equation has No real electrons, so useless. ]

(Fig.9)   Simple useful model is impossible without real electrons.

As I proved above, it is impossible to find exact solution in multi-electron atoms in Schrödinger equation.

Quantum mechanics just chooses artificial fake solution in each atom, which method is completely useless.

In applied physics, they use density functional theory (= DFT ), which also chooses artificial fake Coulomb energy term V.

Each time we deal with different atoms, we have to choose different artificial fake solution in vain.

This is the reason why quantum mechanics is useless forever in applied science such as medicine, and it lacks reality.

 

Only hydrogen atom is solvable.

[ Quantum mechanics can solve only one-electron hydrogen. ]

(Fig.10)  Kinetic + potential energies = total energy E

Under the present science, Schrödinger equation in quantum mechanics is the only tool to calculate atomic energy.

Unfortunately, Schrödinger equation can solve only one-electron hydrogen atom, cannot deal with other multi-electron atoms.

Total energy E is the sum of an electron's kinetic energy and Coulomb potential energy in Schrödinger equation.

Of course, this total energy E must be conserved (= constant ) in every electron's position.

 

Helium has No exact solution.

[ Schrödinger equation of Helium cannot be solved. ]

(Fig.11)  ↓ Helium has No solution ( = No wave-function ψHe )

Schrödinger equation of Helium with two electrons cannot be solved (= Schrödinger Helium has No exact solution ).

Helium potential energy consists of three terms.
Two of them are Coulomb attractive energies between each electron and Helium nucleus (= -2/r1,  -2/r2 in Fig.11 ).

The third term is Coulomb repulsive energy between two electrons.
It includes the variable r12, which represents the distance between two electrons.

 

Choose approximate (fake) Helium solution.

[ Helium solution consists of two hydrogen atoms ? ]

(Fig.12)  ↓ Helium approximate solution (= wavefunction )

Schrödinger equation of Helium cannot be solved.
So we need to choose some approximate (= fake ) Helium solution (= trial wavefunction ).

Ths simplest Helium solution consists of two hydrogen atoms 1 and 2.

After choosing the fake Helium solution and inserting it into Schrödinger equation, we integrate it instead of solving it ( this p.2 ).

By adjusting parameter α, the total (fake) energy E can be lowered.

But this simplest Helium solution cannot get exact Helium energy ( this calculated energy E becomes -77.4 eV which is higher than actual Helium energy -79.0 eV, see this p.4 ).

 

Wrong trick in quantum mechanics.

[ Quantum mechanics relies on "wrong math" in Helium. ]

(Fig.13)  ↓ Hylleraas (fake) Helium wavefunction includes r12

To lower the Helium total energy, quantum mechanics has to rely on wrong math trick, which proves quantum mechanics is wrong.

Instead of the simplest approximate Helium solution (= just two hydrogens ), they use Hylleraas Helium solution which is a little more complicated including r12 (= distance between two electrons ).

This new fake Helium solution including r12 gives better (= lower ) total energy than the simplest solution ( this new Hylleraas solution gives -78.7 eV of Helium total energy, this p.8, which is still slightly higher than the actual Helium energy ).

But in fact, quantum mechanics depends on wrong math trick when this new Hylleraas Helium solution is used.

Kinetic energy of Schrödinger equation is expressed as the second derivative.

This kinetic energy term always gives "unreal negative kinetic energy" which is inversely proportional to the square of distance between two electrons ( ~ 1/r122).  ← this unusual term doesn't exist in the nature.

For the total energy to be conserved, the kinetic energy must cancel out the Coulomb potential energy which is inversely proportional to r12 (= 1/r12 ), Not to the square of r12 ( ~ 1/r122).

This is a wrong and unfair math trick, because the negative kinetic energy inversely propotronal to the square of r12 can unnaturally lower the Helium (fake) total energy in a wrong way.

Because it violates total energy conservation ( negative 1/r122 kinetic energy term cannot cancel Coulomb potential term 1/r12 ).

This is the trick by which quantum mechanics can seemingly get Helium energy value close to the experimental value.

But this deceptive quantum method sacrifices Helium total energy conservation (= kinetic energy + Coulomb potential energy cannot be constant E in this method )

Getting better energy value by deliberately violating total energy conservation (= lowering kinetic energy by dishonest method ) is physically false and inconsistent.

 

The origin of negative kinetic energy.

[ Dirty trick in quantum mechanics. ]

(Fig.14)  ↓ Hydrogen 2p wavefunction.

Unsolvable Schrödinger equation of Helium relies on "dirty trick" to lower its total energy using "negative kinetic energy" inversely proportional to the square of distance r12.

Because negative kinetic energy term inversely proportional to the square of distance (= -1/r2) can be lower than the term inversely proportional to the distance (= -1/r  = Coulomb potential term ).

What's the origin of this nonphysical negative kinetic energy ?

This strange negative kinetic energy is necessary to cancel positive angular kinetic energy which increases inversely proportional to the square of distance (= 1/r2 ) in hydrogen 2p wavefunction.

Hydrogen 2p wavefunction consists of radial (= re-r ) and angular parts (= cosθ ).  See this p.5 angular momentum l=1.

Kinetic energy (= second derivative ∇2 ) of the angular part (= cosθ ) in Hydrogen 2p wavefunction becomes inversely proportional to the square of distance (= l(l+1)/r2,  see this p.5, this p.9 ).

For hydrogen total energy to be conserved (= E is constant ), this angular kinetic energy must be canceled out by corresponding negative kinetic energy inversely proportional to the square of r ( 0 = 1/r2-1/r2 ) in radial part.

Quantum mechanics uses only this radial part of negative kinetic energy in Hydrogen 2p wavefunction, omitting angular part (= spherical harmonics ) to lower Helium total energy in a dishonest way.

Of course, this Schrödinger Helium cannot conserve total energy E (= Not constant ), so physically wrong.  This is the dirty trick of quantum mechanics, which is Not "successful" at all.

 

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2018/8/20 updated. Feel free to link to this site.