Chapter 521 The incredible wave equation! The mystery of wave function! Meet the Ancestor Bruce for three years!
In real history, Schrödinger has achieved three academic achievements in total.
The most well-known of them and is well-known to ordinary people is of course "Schrödinger's Cat".
It is certain that Schrödinger himself does not like raising cats.
So, why he used cats as an example, can only rely on the speculation of future generations.
Given that his love history was too rich, everyone naturally thought of the cat.
But this doesn't matter.
Because Schrödinger's cat conjecture is countless times more mysterious than the cat itself.
Some people probably really know what this cat is talking about.
Schrödinger's Cat was a thought experiment proposed in 1935.
Its purpose is not to prove the correctness of quantum mechanics.
But it is to refute the interpretation of the essence of quantum mechanics by the Copenhagen school represented by Bohr.
The reason why Schrödinger's cat is famous is that it brings human consciousness into observations of the material world for the first time.
This triggered a great academic debate on consciousness and objective existence.
To this day, this question still has no explanation that convinces everyone.
(Don't worry, I'll explain Schrödinger's cat in detail later, it's really incredible.)
The foundation of Schrödinger's cat is Schrödinger's second greatest achievement: the wave dynamics equation, also known as the Schrödinger equation.
Its appearance has truly entered the golden moment of quantum mechanics!
Arosa, Switzerland.
Schrödinger wrote the wave equation in one breath in a state of nearly enlightenment.
Then, he felt a sense of weakness in his body and even his soul.
It seems that all his life's energy was exhausted at that moment.
However, no matter how tired he was, he still had a childish smile on his face.
He glanced gently at Talia, who was sleeping like a cat.
Immediately, the Sage Mode made him focus on the equations he wrote again.
As shown in the figure, this is a second-order partial differential equation.
This formula that looks like alien characters is condensed by Schrödinger's lifelong essence.
Each symbol has its own meaning.
Analyze from left to right:
i: imaginary unit; i=-1.
: Reduced the Li-Planck constant, pronounced as "h-la", =h/2π.
ψ: a wave function, which describes the change of the state of a particle with space and time; it is generally written as ψ(r, t), r represents the coordinate position, and t represents time.
t: Time unit.
m: The mass of particles.
▽: Laplace operator, which represents the divergence of the gradient, does not need to be understood.
V(x): potential field function, describing the energy distribution of the environment in which the particle is located.
In addition, to the right of the equation, the entire part in brackets: (-/2m)▽+V(x).
It represents the total energy (kinetic energy + potential energy) that the system has.
In real history, this equation is a basic assumption of quantum mechanics.
Yes, you read it right, it is not a law, but a hypothesis, or axiom.
When students in later generations study, the textbooks will directly give this equation and just accept it unconditionally.
Because the wave equation is not deduced through theory, but is generated out of thin air.
Schrödinger was unable to give a mathematical proof.
Its correctness can only be verified by experiments.
Luckily, all experiments in later generations have proved that this equation is completely correct.
So, I have to sigh that there are indeed incredible geniuses in this world.
At this moment, Schrödinger himself couldn't believe it.
He woke up from that magical state and realized that he had created an incredible theory.
He wrote this equation directly without any derivation.
The wave equation is expanded on the basis of de Broglie's material waves.
Therefore, it can not only describe the movement of electrons, but also the movement of all microscopic particle systems.
"Oh! God!"
"If it was wrong, I would die immediately!"
After writing the equation, Schrödinger did not accomplish it.
He also needs to use this equation to solve real-life problems.
At least through this wave equation, everything about the old quantum theory can be derived.
At this time, Schrödinger took his pipe and paper and walked out of the villa carefully.
He came to the side of Lake Ober and sat down in a chair.
The high sky, floating white clouds, flying birds, and azure lake water.
The scenery that I felt was boring before was now like a fairyland on earth in his eyes.
His heart calmed down and he began to think again.
The first step is that he needs to explain this equation.
The core of the wave equation is the wave function ψ(r, t).
The solution to this equation requires the ψ(r, t) that meets the conditions of the equation.
For example, for example, x+1=2.
Its solution is very simple, that 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, with the change law of spatial parameter r and temporal 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.
At this point, there is no problem.
However, when explaining the meaning of the wave function itself next, Schrödinger made a mistake.
Even he himself knew about this mistake, and he didn't even think it was a mistake.
Based on this mistake, it will trigger a big debate.
There is thus the famous saying "Schrödinger does not understand Schrödinger equation."
At this moment, in the center of calm Lake Ober, an unknown big fish suddenly jumped out of the water.
Then, the big fish fell heavily into the water.
The waves of water it sways, centered on itself, spread to all directions, as if the whole world was vivid.
Schrödinger's heart moved when he saw this scene.
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, and there is also the wave function ψ water (r, t) in the equation.
ψ water (r, t) represents the shape of the water wave at a certain moment.
As shown in the figure:
When time t=1s, the shape of the water wave is the one above.
The amplitude of the position where the x1 point is located is A.
When time t=10s, the shape changes to the one below because the water waves are constantly propagating forward.
At this moment, the amplitude of the position where point x1 is located becomes -A.
Therefore, the wave function ψ water (r, t) can describe the system of water waves.
As long as we know it, we can calculate the amplitude of any point at any moment.
This is the explanation of wave functions in classical physics.
Schrödinger thought to himself: "The wave function of electrons ψ(r, t) represents the real electron wave."
"Electronic waves are the same as water waves, It is really fluctuating, it is a real wave."
Not only that, he even went further in de Broglie's theory of material waves.
"In addition, electrons can only be waves, they have no particle nature,"
"The reason why we detected the particle nature of electrons in our experiments was that we detected the wave packets of electron waves."
< br>The so-called wave packet, vividly understanding, means treating the curve in the above picture as a whole.
It shows particle nature. Schrödinger has fallen into a mysterious state.
Maybe Heisenberg's matrix mechanics had a great impact on him.
So, he wanted to remove all the parts about particles in his fluctuation equation.
In other words, he even felt that De Broglie's theory of matter waves was wrong.
"Everything is fluctuating" becomes "everything is fluctuating".
Schrödinger is even more extreme!
Heisenberg said that electrons are particles, so he insisted on saying that electrons are waves!
At this moment, Schrödinger was ambition and wanted to compete with Heisenberg for some reason!
"Look at who is the leader of the Institute of Quantum Research!"
The above is Schrödinger's 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 wind" his wave function would cause.
No mistakes, one poem, one post, one content, one in 6, one book, one bar, one read!
Next, Schrödinger used his wave equation to deduce the conclusion of quantum theory from scratch.
He calculated while smiling.
Because the wave equation is too simple compared to matrix mechanics.
For physicists, the wave equation belongs to the thing one or two hundred years ago.
If you don’t know this basic skill, you will not deserve to be called a physicist.
Like matrix mechanics, the wave equation can directly deduce all quantization conditions in hydrogen atoms.
However, Schrödinger frowned slightly when dealing with the fourth quantum number electron spin.
"Slightly deficient."
There are still some problems when deducing electron spins in his wave equation.
Schrödinger just pondered for a while, then didn't take it to heart.
It is normal for the theory to have flaws, and perhaps there is something he overlooks.
Soon, he became excited again.
Because his theory has a more significant advantage than matrix mechanics, in addition to being simple.
That is the visual picture!
In matrix mechanics, the behavior of electrons is purely mathematical operations.
It is intermittent and discontinuous.
Physicists cannot imagine what electrons have experienced.
But the wave equation treats electrons as a continuous fluctuation.
In this way, physicists can imagine in their minds how electrons work. "Oh, electrons are like water waves, rippling everywhere inside atoms."
There is a judgment on the level of height!
Schrödinger has full confidence that his wave dynamics will definitely replace matrix mechanics.
He even named his theory directly. "What a wonderful name!"
The next ten days, Schrödinger and Talia kept getting tired of being in the villa.
He enjoyed a wonderful life while organizing his wave dynamics into a paper.
Before publishing, he needs to read the paper to Professor Bruce.
This is the minimum respect.
In addition, Schrödinger is very good at handling human feelings and worldly styles.
He also plans to send a copy to Professor Planck to seek the other party's evaluation.
Because he cannot stay in the Institute of Quantum Research all the time, he will be independent sooner or later.
And he hopes to work at the University of Berlin in the future.
So of course, we must establish a good relationship with Professor Planck.
After all, as he is, it is very difficult to find an important position in the top universities in Britain and France.
Soon after Schrödinger's holiday ended, he was finally going back to the UK.
"Talia, I will miss you."
"If I hadn't been you this time, my world would be full of darkness."
"It is you who brought me light and warmth."
Pooh!
Talia smiled and was unparalleled.
She deliberately tentatively: "Oh, dear, since I am so important to you, why don't we be together forever."
"I will give you more inspiration."
Faced with such provocative words, Schrödinger's will was like a rock and remained unmoved after success.
"Talia, you are a free bird in heaven. How can I bear to restrain you?"
"Next, I will start challenging this world!"
<< br>"This is the noblest cause of a man!"
"I must do my best and focus without distractions!"
Such pretentious words made Talia feel a little more heart-warming.
She admired the man in front of her extremely.
Even if she is about to separate at this moment, she will always remember the beauty of this period. "Goodbye, Schrödinger."
——
June 15, 1923.
Schrödinger returned from vacation, and he immediately stepped into the physics temple that countless people dream of with his paper:
The Office of the Director of the Quantum Research Institute!
Li Qiwei looked at the reborn Schrödinger in front of him and couldn't help but sigh.
Sure enough, truth is a scientist's dream, which makes people feel infinitely charming.
After reading the paper seriously, he smiled and said, "This is the idea of a genius."
"Schrödinger, you do better than I thought you did Countless times."
"This paper will surely open a new chapter in quantum mechanics."
When Schrödinger heard this, he was shocked and extremely excited.
His body trembled slightly from excitement, and there was an irresistible light in his eyes.
It is the light of wildness, the light of desire, the light of truth.
But soon, he regained his expression, stood up solemnly, and said gratefully from the bottom of his heart: "It is more important to be able to get your recognition than half of the world's recognition of me ! ”
"Without your inspiration, I would never have thought of thinking about the wave equation of electrons, and this paper would not be available."
"Thank you, Professor Bruce."
After saying that, he bowed deeply .
At this moment, in Schrödinger's heart, 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 all living beings.
Bruce was perfectly capable of turning these ideas into theory, but he didn't do that.
Schrödinger vaguely knew something that the majestic man in front of him was pursuing a more magnificent ambition.
That is the ultimate theory that transcends Professor Einstein's theory of unity!
Represents the end of physics!
That is the so-called genius Schrödinger, who can't be seen at all!
Quantum mechanics is just one link, perhaps the most important link.
It is better to say that Professor Bruce is guiding the younger generation, he is preaching the world!
Schrödinger is full of expectations for the future.
Professor Bruce has guided him to see higher scenery, and he must grasp it well.
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, and seemed to be talking to Schrödinger.
"The drama of quantum mechanics is finally about to begin!"
(This chapter ends)