Great Country Academician

"Brother Chuan is here."

"Brother Chuan, I heard you went to the math competition this year. How is it going over there? Is it fun?"

"I heard that this year's math competition is very difficult. There are only twelve people who got full marks in the provincial competition. Brother Chuan is one of them!"

"More than that, don't forget about our Wujing Provincial Competition, Brother Chuan also got a perfect score."

"Awesome! As expected of Brother Chuan, it's the last time. Brother Chuan definitely wants to win a double gold medal."

At Yali Middle School, with the arrival of Xu Chuan, the provincial training team quickly became lively, and all the students in the classroom gathered together.

As a person who has entered the provincial team for three consecutive years, most of the students in front of him know Xu Chuan.

After all, those who can enter the provincial team are basically sophomores and seniors. The students who came to experience the competition in the first year of high school also got to know this great figure under the introduction of the old students.

A player who can win a gold medal in a world-class competition in the second year of high school, in the eyes of all the students who participated in the competition, that cliff is a god who is too strong.

"Yo, Xu Chuan is here."

Outside the noisy classroom, a somewhat unexpected voice came.

Xu Chuan turned his head to look, and greeted the person respectfully when he saw the person coming.

"Teacher Xu."

Xu Cheng looked at the student in front of him with a smile and nodded as a greeting.

The student in front of him was taken by him last year, but I heard that he participated in the math competition this year, and got full marks to enter the provincial team.

And I heard from the old guy at Shujing that his math ability is stronger than his physics ability.

Xu Cheng scoffed at this statement.

Don't you just want to rob people, why are you making so many tricks?

It's not that there are people who participate in the math competition and the physical competition at the same time, but those who can enter the provincial team and enter the golden autumn camp and winter camp at the same time, in recent years, there have been no people in southern Shonan, but there are a few in Mingyue City and Midtown.

However, there is no one in China that can win gold medals in both IMO and IPHO in the same year.

Those who can be selected into the national training teams of Mathematics and Wujing in the same year, from the beginning of the formation of domestic teams to participate in international competitions in the 1990s to the present, have only two or three people in more than 30 years.

After all, there is still a big gap between the number competition and the physical competition. It is too difficult to reach the top in both aspects.

Xu Cheng is still looking forward to Xu Chuan.

He is very clear about the physical ability and learning ability of this student. After one and a half years of study, he can win the gold medal on IPHO. This year, it can be said that he can win another gold medal firmly.

Even the first place winner is not impossible to look forward to.

However, anticipation was nothing but anticipation. Xu Chuan was still a little dissatisfied when he went to engage in a math competition.

After all, human energy is limited. If you do mathematics, you will spend less energy on physics.

So he planned to use the questions to test it. If there was no progress, don't blame him for practicing ruthlessly to death in the next month.

Such a good genius, don't come to study physics, but to study labor model mathematics?

And it's obviously a genius discovered in physics, so what's the point of robbing someone in the middle of mathematics?

Don't even think about it!

"Come on, come on, do the first question, and let me see your study results in the past year."

After saying hello, Xu Cheng picked up the chalk on the podium, stood in front of the blackboard and thought for half a minute, and then started to write.

"Bosons do not obey the Pauli exclusion principle and, at low temperatures or high densities, undergo dramatic Bose-Einstein condensation (BEC) phenomena."

"It's an interesting quantum collective state achieved through a phase transition."

".BEC occurs when the de Broglie wavelength corresponding to the root-mean-square velocity of the atoms is roughly comparable to the characteristic distance between particles in a gas.

1. For non-interacting 87Rb gas atoms in thermal equilibrium, write down the expressions of their typical momentum p and de Broglie wavelength λdB, expressed by atomic mass m, temperature T and physical constants.

2. Calculate the functional relationship between the typical distance l between particles in the gas and the particle number density n. Then deduce the critical temperature Tc expression, expressed by atomic mass, density and physical constants.

Third, in order to realize BEC in the laboratory, experimenters need to reduce the temperature of the gas to Tc=100nK.

If BEC occurs at this temperature, what is the number density nc of 87Rb gas? For the convenience of comparison, the number density n0 of an ordinary ideal gas at standard temperature and pressure is also calculated, that is, T0=300K, p0=105Pa, it can be assumed that the mass of an atom is equal to 87 atomic mass units (mamu), what is the density n0 of an ordinary gas How many times is it nc? .

Under the podium, a group of students were all stunned, wondering whether they had crossed over on the first day of training.

What is this writing? No matter how you look at it, you can’t understand it?

Only a few students frowned tightly, staring at the topics on the blackboard that almost occupied the entire blackboard.

"This question is relatively difficult, and some mathematical knowledge is applied. You can use it as an extracurricular test question. If you are interested, you can try to solve it, except for Xu Chuan. Give me the answer tomorrow morning. I heard that you are competing for the provincial exam. It shouldn't be difficult for you to get full marks."

Xu Cheng threw the chalk tip in his hand on the podium, stared at Xu Chuan and said.

The corner of Xu Chuan's mouth twitched, and he probably understood that this was Xu Cheng's dissatisfaction with him for participating in the math competition.

But to be serious, ordinary high school students may not be able to solve this problem even if they have the ability to enter the national training team.

The difficulty is almost the same as that of IPHO. Putting it on IPHO, it is almost the type of the penultimate big question.

This question is about Bose-Einstein condensation. The whole question has three parts. The first part is not very difficult. It can be solved with a certain physical foundation.

But the difficulty of the second and third small parts rises linearly, which is comparable to sitting on a rocket. Whether it is to find the root-mean-square velocity based on the average kinetic energy of atoms, or to find the de Broglie wavelength after finding the momentum, the difficulty is not ordinary. High school kids can handle it.

And the difficulty of finding the distance between particles in the third step has to be improved to a higher level.

If the first question is 1+2=3, then the difficulty of the second and third questions will directly soar to prove that 1+2=3.

Compared with the mathematics competition questions, the calculation amount of this question is actually not large, but it requires a lot of logical ability and application ability of the solver.

But this is the ability to learn physics.

After all, there is a big difference between physics and mathematics.

In the process of systematic learning, the difficulty of mathematics lies in the cultivation of thinking, and the difficulty of physics lies in the application of knowledge and methods.