Chapter 63 Inversion Invariance of Laplace's Equation
After class, Xu You was the first to rush to the podium.
"Teacher, Laplace's equation is invariant to inverse transformation, right?"
Cao Quanli was also stunned when he heard Xu You's question.
In Cao Quanli's teaching career, he had never heard of such a thing.
"Xu You, what are you talking about?"
If someone else asked this inexplicable question, Cao Quanli would even directly tell him not to study this matter as it sounded a bit unorthodox.
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 a full score.
In the year when Cao Quanli won the championship, he did not get full marks.
Cao Quanli also worked on this year's final questions himself.
It is absolutely impossible to get full marks.
For a child like Xu You, Cao Quanli could only express respect.
"Teacher, let me write it directly on the blackboard."
"Well, write it down and let me see."
During normal break 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 atmosphere of the end of get out of class in the classroom.
Everyone looked at the blackboard, curious about what Xu You and Cao Quanli were discussing.
"Hey, do you know what that Labu Labu La that Youshen is talking about is?"
After listening to the general idea, Luo Wenkun asked Lin Shi in confusion.
Lin Shi shook her head, also looking puzzled.
After that, Xu You wrote down his entire derivation process.
Because this classroom has four large movable blackboards, there will be no situation where there is not enough space to write.
Xu You can write with confidence.
"Teacher, we use the inversion method to deduce that the Laplace equation is inverse transformation invariant. The inversion method is also in the textbook, in the "Electrodynamics of Continuous Media". I remember it was page 13, but there was no proof process on it. I just proved it."
"The inversion method... there does exist such a method."
Cao Quanli tried hard to recall and did have some impression of this method.
As for whether it is on page 13 of the book "Electrodynamics of Continuum Media".
Cao Quanli naturally couldn't remember it for sure.
"From the Laplace equation in the spherical coordinate system, and two inverse transformation expressions, we can derive this equation..."
"For the angular part of Laplace's equation, we have the same result..."
"This gives us the inverse transformed Laplace equation..."
Xu You explained to Cao Quanli 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 attending a mathematics competition class.
"Compared with the original Laplace equation, we can see that after eliminating the coefficients, the two have exactly the same form, and the relationship between the solutions can be determined based on the inverse transformation formula."
After explaining the entire derivation process, Cao Quanli still seemed to be confused.
As for the students under the podium...
I have no idea what Xu You is talking about.
"Xu You, are you using the number competition method?"
"Yes, these are some of the methods I learned in the math competition. Mathematics and physics are interconnected. Teacher, it should be okay 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 studied math competitions specifically and does not know much about some of the methods used in math competitions.
After all, if Xu You’s method is really correct, it would indeed save a lot of time in solving the problem.
Everyone felt secretly delighted when they saw this scene.
Isn’t Cao Quanli usually quite awesome?
Why is it that I don’t dare to answer Xu You’s question this time?
Lin Shi also felt a lot more comfortable.
Sure enough, Xu You can never be viewed with a normal perspective.
Even Cao Quanli, the head coach of the national team, could not judge whether Xu You's proof process was correct.
"Well, I'll find a teacher to confirm it. I can't guarantee the accuracy of the mathematical method used in it."
Cao Quanli finally put aside his pride and decided to seek off-field assistance.
After a while, another teacher came into the classroom.
"This is Mr. Qiao Sen, a former champion of the Physics Competition, and a double national champion of the Physics Competition and Mathematics Competition. He has also coached many national teams. Mr. Qiao Sen, please take a look at this student's derivation process."
This kind of thing involves relatively complex mathematical knowledge and is indeed difficult to understand for people who have not studied math competitions.
Teacher Qiao Sen hadn't even looked at the question yet, but just glanced at the solution process on the blackboard and his face showed joy.
"Child, is this your proof?"
Xu You nodded upon hearing this.
"Just now during class, I suddenly thought of this method and proved it. I don't know if it is correct or not, and I don't know if it can be used."
Hearing Xu You's words, Qiao Sen laughed even more happily.
"Haha, we finally have a talented person in China who can learn both physics and mathematics well! Not bad, not bad, the young are formidable!"
"Teacher Qiao, have you seen this method?" Cao Quanli asked in surprise.
"If I understand correctly, this is proof that Laplace's equation is invariant under reverse transformation, right?"
"Yes, it's that Labrador. Does it need a certificate of sex change?" Luo Wenkun answered quickly.
When people heard Luo Wenkun's words, there was a burst of laughter in the classroom.
"Seven years ago, when I was teaching an electromagnetism problem, a child also derived such a property. However, because the threshold is too high, it is not recommended for students who have not been exposed to mathematics competitions."
"In other words, there is no problem with this process?" Cao Quanli asked in surprise.
Qiao Sen carefully read the entire proof process 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 you fully prove this process on the test paper, you will not lose a single point. This method is indeed much faster than the conventional method."
Seeing Qiao Sen so sure, Cao Quanli no longer had any worries.
"Since Teacher Qiao said it's OK, then it can definitely be used. Teacher Qiao, should this method be promoted as a common solution?"
"If you have never learned math competition, there is no need to master this method. It involves too much math competition knowledge. It is enough for everyone to know that there is such a method, and there is no need to master it."
Although the entire proof process is not extremely long, it is indeed difficult to memorize it in its entirety if you don’t understand it.
If the proof is wrong due to problems in some intermediate processes, the result would be more trouble than gain.
"That's true. I'll wipe it off then."
Hearing Qiao Sen say this, Cao Quanli felt that he had regained some face.
After all, he wouldn't be able to explain it clearly even if you asked him to.
Just think of it as Xu You’s proprietary solution.
"Wait a minute, teacher, don't wipe it yet!"
