Quantum mechanical fairy tale: John and Jan's story A possible burgioning formation of a chemical bond between two hydrogen atoms

[MitsuruYamada]

Once upon a time, there was a prairie.

There were two houses on the prairie separated by a certain distance.

In the Eastern house, a girl called Mary was living.  She was five years old.

In the Western house, another girl called Nelly was living.  She was five years old too.

Around the Mary's house, a boy whose name is John was playing and running.  He was five years old.  He liked Mary.  So he was always longing for her and running around her house.

Around the Nelly's house, another boy whose name is Jan was playing and running. He was five years old.  He liked Nelly.  So he was always longing for her and running around her house.

One day, a voice of God in the heaven sounded.  "Let there be interactions!"

It was a spell called as Coulomb's magic.

Untill then the most beautiful girl for John was Mary.  Untill then the most beautiful girl for Jan was Nelly.

Suddenly John noticed another girl Nelly.  Although she was a little bit far from him, she looked as beautiful as Mary.

The same thing has happened on Jan.  He suddenly noticed another girl Mary.  Although she was a little bit far from him, she looked as beautiful as Nelly.

The two boys became to be attracted by the two girls simultaneously.  The two girls had beauty called "positive charge."  On the other hand, the two boys had vitality called "negative charge."  The both of the two boys became to be puzzled and perplexed.  They both were embarrassed.  "What should I do?"

The two houses that the two girls lived in were about 2000 fold heavy than the weight of John or Jan.  So the two girls could not begin to move easily.  But the boys were light and swift.  So the boys began to employ another course of action.

Actually, the two boys were perplexed because they had the same "negative charge" which caused one to avoid the other one.  The boys shouted "How should I do?  I like both of Mary and Nelly!  The other boy does too. But I must be careful to avoid him!"

On the prairie, there was a law called "Time-dependent Schroedinger equation."  Everything on the prairie had to obey that law.  The law "Time-dependent Schroedinger equation" determined the course of action of the two boys.

After severalty days, the two boys found themselves to their surprise, that they were now occupying the same localized region between the girl's houses, and are staying near each other boy despite the Coulomb's magic!

Since the time when two boys began to stay together between the girl's houses, the two girls began to feel little hesitation to move toward the direction of the other girl's house.  In the prairie, there was a peace again.  All of two boys and two girls were happy again now.

This was the story of burgioning of a chemical bond formation.  This is the primordial mechanism of how the two hydrogen atoms begin to form a chemical bond.

The ultimate key ingredients were orders predetermined by the law of "Time-dependent Schroedinger equation."

The End

An anonymous writer

September 1, 2012

[MitsuruYamada]

Dear readers of my blog,Sirs,

This is the author.

How funny is my spell miss!  "burgioning" must be "burgeoning" of course!

Though my blog title is "fairy tale", it actually intorduced a result of computer simulation on the behavior of two electrons in two-dimensional space as you must have already noticed by the attached zip file.

I would repeat the initial conditions of the simulation.

First, the lattice space is between +6 and -6 in x-dimension and +6 and -6 in y-dimension.  61 lattice points were distributed on each dimensions.  Second, fixed protons Mary and Nelly were placed on the x-axis separated by a distance NUCSEOP=3.   Third, the fine boys John and Jan are assigned by arbitrary Gaussian wave functions each of which is centered on Mary or Nelly.

Then I started the Schroedinger equation time development process.

But the interaction potential was roughly assumed in that it has finite Coulomb depth.  Arbitrarily the depth was assigned 1/epsilon, where epsilon=1/100a, where a is the lattice constant.  And the time slice was 0.001.

As the result of simulation, three curious points were found.

1. Both of John and Jan displace to the center region by spooky fashion.

John or Jan's light of wave function moved and reappeared at the central region(origin region) discontinuously.

2. Plotting the track of the x-coordinates of both of John <X1> and Jan <X2>, we cannot expect their approaching process to reverse.  That is, the time developmental process seems irreversible as if it represents an adhesive bonding process.

3. I meant the relative distance of the two electrons John and Jan by a notation <R1-R2>.

As the time developmental process proceeds, it became extremely small value.  What does this mean?  Two electrons at the same spatial position?

As to point 1, I am now pondering a movement of 4-dimensional fruid in the 4-dimensional space.  It cannot be imagined by us who are living in the 3-dimensiona space, but it might allow the such spooky banishing phenomenon at the starting point and reappearing phenomenon at the central objective region.

As to point 2, almost of us are taught the doctrines of covalent bonding and ionic bonding and their mixes.  But we cannot image the covalent bonding picturesquely.  On the contrary, this spatial gathering of the two electrons looks as if it works like a glue that attracts both of Mary and Nelly vividly and physicaly intuitively.

As to point 3, the paradoxical situation seems as if forms the foundation of the principle of the chemical bonding that supports the point 2.

How do you think or look at these strange results?

I am now continuing this research now.

I am waiting your direct advices eagerly.

The many-electron maniac

September 21, 2012