1900: A physics genius wandering around Europe

Chapter 521: The incredible wave equation! The mystery of the wave function! The third meeting with Bruce the Elder!

In real history, Schrödinger had three major academic achievements.

The most famous and well-known one among ordinary people is of course "Schrödinger's cat".

What is certain is that Schrödinger himself did not like to keep cats.

Therefore, why he used cats as an example can only be guessed by future generations.

Given his rich love history, people naturally got the cat wrong.

But that's not important.

Because Schrödinger's cat conjecture is countless times more mysterious than the cat itself.

I guess few people really know what this cat is talking about.

Schrödinger's cat is a thought experiment proposed in 1935.

Its purpose is not to prove the correctness of quantum mechanics.

Rather, it was to refute the Copenhagen school's interpretation of the essence of quantum mechanics, represented by Bohr.

Schrödinger's cat is famous because it brought human consciousness into the observation of the material world for the first time.

This triggered a major academic debate about consciousness and objective existence.

To this day, there is still no explanation that convinces everyone.

(Don’t worry, I will explain Schrödinger’s cat in detail later. It is truly incredible.)
The basis of Schrödinger's cat is Schrödinger's second great achievement: the wave mechanics equation, also known as the Schrödinger equation.

Its appearance has truly ushered in the golden age of quantum mechanics!
Arosa, Switzerland.

In a state of near enlightenment, Schrödinger wrote out the wave equation in one breath.

Immediately, he felt his body and even his soul becoming weak.

It was as if all the energy in his life was exhausted at that moment.

However, no matter how tired he was, he still had a childlike smile on his face.

He glanced tenderly at Talia, who was sleeping like a cat.

Then, Sage Mode allowed him to focus again on the equation he had written.

As shown in the figure, this is a second-order partial differential equation.

This formula, which looks like alien language, is the essence of Schrödinger's life.

Each of these symbols has its own meaning.

Analyze from left to right:
i: imaginary unit; i=-1.

: Reduced Lie-Planck constant, pronounced "hba", =h/2π.

ψ: wave function, describing the change of particle state with space and time; generally written as ψ(r, t), where r represents the coordinate position and t represents time.

t: time unit.

m: mass of the particle.

▽: Laplace operator, which represents the divergence of gradient, does not require understanding.

V(x): Potential field function, which describes the energy distribution of the particle's environment.

In addition, on the right side of the equation, the integral part within the brackets is: (-/2m)▽＋ V(x).

It represents the total energy (kinetic energy + potential energy) possessed by the system.

In real history, this equation is a fundamental assumption of quantum mechanics.

Yes, you read it right, it is not a law, but a hypothesis, or an axiom.

When future students study, the textbooks will directly give this equation and they will just accept it unconditionally.

Because the wave equation is not derived through theory, but generated out of thin air.

Schrödinger was unable to provide a mathematical proof.

Its correctness can only be verified by experiment.

Fortunately, all subsequent experiments have proved that this equation is completely correct.

Therefore, I have to sigh that there are indeed incredible geniuses in this world.

At this moment, Schrödinger himself couldn't believe it.

After he woke up from that magical state, he realized that he had created an incredible theory.

He actually wrote out the equation directly without any derivation.

The wave equation is an extension of the de Broglie matter wave.

Therefore, it can not only describe the movement of electrons, but also the movement of all microscopic particle systems.

"Oh! God!"

"If it's wrong, I'll die instantly!"

Having written down the equation, Schrödinger was not done.

He also needs to use this equation to solve real problems.

At least through this wave equation, all the contents of the old quantum theory can be derived.

At this time, Schrödinger took his pipe and thesis and walked out of the villa carefully.

He came to the side of Lake Ober and sat down on a chair.

The high sky, the floating white clouds, the flying birds, the blue lake.
The scenery that he had previously considered dull now looked like a paradise on earth in his eyes.

His heart calmed down and he began to think again.

The first step was to explain the equation.

The core of the wave equation is the wave function ψ(r, t).

The solution to this equation is to find ψ(r, t) that meets the conditions of the equation.

For example, x+1=2.

Its solution is very simple, which is x=1.

Now, the solution to the wave equation is no longer a simple number, but a complex function: ψ(r, t).

ψ(r, t) describes the state of microscopic particles, which changes with the spatial parameter r and the time parameter t.

As long as the initial conditions and boundary conditions are given in the equation, the expression of the ψ(r, t) function can be calculated.

Up to here, no problem.

However, when it came to the next step of explaining the meaning of the wave function itself, Schrödinger made a mistake.

He himself didn't even know about this mistake, and he didn't even think it was a mistake.

Based on this mistake, a big debate will arise.

Hence the famous saying "Schrödinger did not understand the Schrödinger equation".

At this moment, in the center of the calm Lake Ober, an unknown big fish suddenly jumped out of the water.

Then the big fish fell heavily into the water again.

The waves it created spread in all directions with itself as the center, as if the whole world had come alive.

When Schrödinger saw this scene, he was moved.

He found an explanation for the electron wave function!

He compared it to the wave equation in classical physics.

It's like the waves in front of you.

Water waves also have their own wave equation, which also contains the wave function ψwater(r, t).

ψwater(r, t) represents the shape of water waves at a certain moment.

as the picture shows:
When time t=1s, the shape of the water wave is the one above.

The amplitude at the location of point x1 is A.

When time t=10s, since the water wave continues to propagate forward, its shape changes to the one shown below.

At this moment, the amplitude at the point x1 becomes -A.

Therefore, the wave function ψwater(r, t) can describe the water wave system.

Once we know it, we can calculate the amplitude of any point at any time.

This is the explanation of wave function in classical physics.

Schrödinger thought:
"The electron's wave function ψ(r, t) represents the real electron wave."

"Electron waves are like water waves. They are real waves."

Not only that, he even went a step further on de Broglie's matter wave theory.

"Besides, electrons can only be waves, they have no particle properties,"

"The reason why we detected the particle nature of electrons in the experiment is that we actually detected the wave packets of electron waves."

The so-called wave packet can be understood figuratively by treating the curve in the above figure as a whole.

It showed particle nature. Schrödinger had fallen into a mysterious state.

Maybe Heisenberg's matrix mechanics had a great influence on him.

So he wanted to eliminate all the particle aspects of his wave equation.

In other words, he even thought that de Broglie's matter wave theory was wrong.

"Everything is in wave" becomes "Everything is wave".

Schrödinger is even more extreme!
Heisenberg said that electrons are particles, so he insisted that electrons are waves!

At this moment, Schrödinger's ambition was running wild and he wanted to compete with Heisenberg!
"Let's see who is the boss of the Quantum Research Institute!"

The above is Schrödinger’s complete explanation of the wave equation he wrote.

He felt it was perfect and impeccable.

"I'm such a genius!"

At this moment, he didn't know what kind of "bloody storm" his wave function would cause.

Next, Schrödinger used his wave equation to derive the conclusions of quantum theory from scratch.

He calculated with a smile on his face.

Because the wave equation is too simple compared to matrix mechanics.

For physicists, wave equations are something that is from a hundred or two hundred years ago.

If you don’t have this basic skill, you don’t deserve to be called a physicist.

Like matrix mechanics, the wave equation can directly derive all the quantization conditions in the hydrogen atom.

However, when dealing with the fourth quantum number, electron spin, Schrödinger frowned slightly.

“It’s a little bit lacking.”

There were still some problems when his wave equation was used to deduce electron spin.

Schrödinger just thought about it for a while and then didn't take it to heart.

It is normal for theories to have flaws, and perhaps there is something he has overlooked.

Soon, he became excited again.

Because his theory, in addition to being simple, has a more significant advantage over matrix mechanics.

That’s visualization!

In matrix mechanics, the behavior of electrons is pure mathematical operations.

It is intermittent and discontinuous.

Physicists cannot imagine what exactly the electron went through.

But the wave equation treats the electron as a continuous wave.

This allows physicists to once again imagine in their minds how electrons work.

"Oh, the electrons are like water waves, rippling everywhere inside the atom."

Sit down!

Schrödinger had full confidence that his wave mechanics would definitely replace matrix mechanics.

He even gave his theory a name.

"What a wonderful name!"

For the next ten days or so, Schrödinger and Talia stayed together in the villa.

While enjoying a good life, he organized his wave mechanics into a paper.

Before publishing, he needs to show the paper to Professor Bruce.

This is the most basic respect.

In addition, Schrödinger has a good grasp of the ways of the world.

He also planned to send a copy to Professor Planck to seek his evaluation.

Because he can't stay in the Quantum Research Institute forever, he will become independent sooner or later.

And he very much hopes to work at the University of Berlin in the future.

So, of course, I have to establish a good relationship with Professor Planck.

After all, with his status, it is very difficult for him to seek an important position in the top universities in Britain and France.

Soon, Schrödinger's vacation was over and he was finally going back to England.

"Talia, I will miss you."

"Without you this time, my world will be filled with darkness."

"You brought me light and warmth."

Boo!
Talia smiled beautifully.

She deliberately tried:

"Oh, dear, since I mean so much to you, why don't we be together forever."

“I will give you more inspiration.”

Faced with such provocative words, Schrödinger, after his success, remained as firm as a rock.

"Talia, you are a free bird in the sky. How can I bear to tie you down?"

"Next, I will start to challenge this world!"

“This is the noblest cause for a man!”

"I have to give it my all and not be distracted!"

Such pretentious words made Talia feel aroused again.

She admired the man in front of her immensely.

Even though they are about to separate now, she will always remember the beauty of this time.

"Goodbye, Schrodinger."
-
1923 6 Month 15 Day.

When Schrödinger returned from vacation, he immediately took his paper and stepped into the temple of physics that countless people dreamed of:

Office of the Director of the Quantum Institute!

Li Qiwei couldn't help but sigh as he looked at the completely transformed Schrödinger in front of him.

Indeed, truth is a drug for scientists, making people radiate infinite charm.

After reading the paper carefully, he smiled and said:

“It’s a genius idea.”

"Schrödinger, you did countless times better than I thought."

"This paper will definitely open a new chapter in quantum mechanics."

Upon hearing this, Schrödinger was shocked and extremely excited.

His body trembled slightly with excitement, and there was an uncontrollable light in his eyes.

That is the light of wildness, the light of desire, the light of truth.

But soon, he regained his composure, stood up solemnly, and expressed his gratitude from the bottom of his heart:
"Your approval is more important than half the world's approval of me!"

"Without your inspiration, I would not have thought of the wave equation for electrons, and there would not have been this paper."

"Thank you, Professor Bruce."

After saying that, he bowed deeply.

At this moment, in Schrödinger's mind, Professor Bruce in front of him was the well-deserved godfather of quantum.

The other party stands at the end of the physical road, overlooking all living beings, but is full of compassion for them.

Bruce had every ability to turn these ideas into theory, but he didn't.

Schrödinger vaguely knew that the tall man in front of him was pursuing greater ambitions.

That is the ultimate theory that surpasses Professor Einstein's unified field theory!
It represents the end of physics!

That was the supreme realm that Schrödinger, the so-called genius, could never reach even with his best efforts!

Quantum mechanics is just one part of it, perhaps the most important one.

Rather than saying that Professor Bruce is guiding the younger generation, it would be more accurate to say that he is preaching to the world!

Schrödinger is full of expectations for the future.

Professor Bruce showed him a higher level of scenery, and he must seize the opportunity.

Always move in the direction of truth!
Under Schrödinger's respectful gaze, Li Qiwei slowly stood up and walked to the window.

He seemed to be talking to himself, but also seemed to be talking to Schrödinger.

"The drama of quantum mechanics is finally about to begin!"

(End of this chapter)