Chapter 63 Inversion transformation invariance of Laplace’s equation

After class, Xu You was the first to rush to the podium.

"Teacher, Laplace's equation is invariant to inversion transformation, right?"

Cao Quanli was also stunned when he heard Xu You's question.

In Cao Quanli's teaching career, he has never heard of such a property.

"Xu You, what are you talking about?"

If someone else had raised this incomprehensible question, Cao Quanli would have even directly told him not to study it, which sounded a bit heretical.

However, if it was Xu You who asked the question, it would be completely different.

In this year's CPhO finals, Xu Youke won the first place in the country with perfect scores.

In the year when Cao Quanli won the championship, he also failed to get full marks.

Cao Quanli also did this year's final question himself.

It’s also completely impossible to get full marks.

For a child like Xu You, Cao Quanli could only show respect.

"Teacher, let me just write it on the blackboard."

"Well, you write it down and I'll take a look."

During normal get out of class time, Cao Quanli would often discuss issues with students.

Cao Quanli would naturally agree to Xu You's request.

At this time, there was no end-of-get out of class atmosphere in the classroom.

Everyone looked at the blackboard, wondering what Xu You and Cao Quanli were discussing.

"Hey, do you know what you are talking about?"

After hearing the general idea, Luo Wenkun asked Lin Shi puzzledly.

Lin Shi shook her head, also looking puzzled.

After that, Xu You wrote out his entire derivation process.

Because this classroom has four large movable blackboards, there will be no difficulty in writing.

Xu You can feel free to write.

"Teacher, you use the inversion method to deduce that the Laplace equation is invariant to inversion transformations. The inversion method is also available in the textbook, in "Continuum Electrodynamics". I remember it should be page 13, but

There is no proof process above, I just proved it."

"Inversion method...there is indeed such a method."

Cao Quanli tried to remember, and he was indeed somewhat impressed by this method.

As for whether it is on page 13 of the book "Continuum Electrodynamics".

Naturally, Cao Quanli couldn't remember it accurately either.

"From the ce equation in the spherical coordinate system, and there are two inversion expressions, this equation can be derived simultaneously..."

"For the angular part of the ce equation, there is also..."

"In this way, the ce equation after the inversion transformation is obtained..."

Xu You explained to Cao Quanli according to the process he wrote on the blackboard.

As he listened, Cao Quanli couldn't help but frown.

For some reason, Cao Quanli always felt like he was listening to a mathematics competition class.

"Compared with the original ce equation, it can be seen that after eliminating the coefficients, the two forms are exactly the same, and the solution relationship can be determined based on the inversion transformation formula."

After explaining the entire derivation process, Cao Quanli looked half-understood.

As for the students under the podium...

I have no idea what Xu You is talking about.

"Xu You, are you using the math method?"

"Yes, they are some methods learned in the math competition. Mathematics and physics are inherently connected. Teacher, it should be no problem to use mathematical methods to help solve physics problems, right?"

At this time, Cao Quanli was also a little embarrassed.

Cao Quanli did not dare to say that Xu You's method was wrong, nor did he dare to say that Xu You's method was correct.

Cao Quanli has not specifically studied math competition and does not know much about some methods in math competition.

After all, if Xu You's method is really correct, it will indeed save a lot of time in solving problems.

When everyone saw this scene, they felt a little happy.

Isn’t Cao Quanli pretty awesome at ordinary times?

Why did Xu You dare not answer this question?

Lin Shi felt a lot more comfortable.

Sure enough, Xu You cannot be viewed with normal eyes.

Even Cao Quanli, the head coach of the national team, could not judge whether Xu You's certification process was correct.

"In this case, I will find a teacher to come and confirm. I am not sure about the mathematical methods used in it."

Cao Quanli finally put down his face and decided to seek off-site assistance.

After a while, another teacher came to the classroom.

"This is Mr. Qiao Sen, who is also a former champion of the Wushu Sports. He is also a member of two national teams in the Wu Sports and has led many national teams. Mr. Qiao Sen, please take a look at this student's derivation process."

It is indeed difficult for people who have not studied mathematics to understand such complex mathematical knowledge.

Teacher Qiao Sen didn't read the question yet, but just looked at the problem-solving process on the blackboard, and his face lit up.

"Child, did you prove this?"

Xu You nodded after hearing this.

"When I was in class just now, I suddenly thought of this method, and I proved it easily. I don't know if it's right or if it can be used."

Listening to Xu You's words, Qiao Sen smiled even more happily.

"Haha, we finally have a good youngster in China who can learn both physical science and mathematics well at the same time! Not bad, not bad, the young ones are to be feared!"

"Teacher Qiao, have you ever seen this method?" Cao Quanli said in surprise.

"If I read it correctly, this is proof that Laplace's equation is invariant to inversion transformations, right?"

"Yes, it's that Labrador's proof of whether he wants to change his gender or not." Luo Wenkun answered quickly.

Hearing Luo Wenkun's words, the classroom burst into laughter.

"Seven years ago, when I was teaching a topic on electromagnetics, a child came up with such a property. But because the threshold is too high, it is not recommended for students who have not been exposed to mathematics."

"In other words, there is no problem with this process?" Cao Quanli said in surprise.

Qiao Sen read the entire proof process carefully again and nodded solemnly.

"There is no problem with the proof process. And I have confirmed that it can also be used on IPhO. As long as this process is completely proved on the test paper, there will never be a point deducted. This method is indeed much faster than the conventional method.

"

Seeing that Qiao Sen was so sure, Cao Quanli no longer had any worries.

"Since Teacher Qiao said there is no problem, it must be possible. Teacher Qiao, should this method be promoted as a commonly used solution?"

"If you haven't studied mathematics, there is no need to master this method. It involves too much knowledge of mathematics. Everyone knows that there is such a method, and there is no need to master it."

Although the entire proof process is not exaggeratedly long, it is indeed difficult to recite it completely if you don't understand it.

If there is a problem in some of the intermediate processes and the proof is wrong, the gain outweighs the loss.

"That's right, then I'll wipe it off."

Seeing Qiao Sen say this, Cao Quanli also felt that he had regained some face.

After all, if you ask him to explain it, he won't understand it.

Just think of it as Xu You’s proprietary solution.

"Wait a minute, teacher, don't wipe it yet!"
Chapter completed!