The next evening, as he walked to the statue of Our Lady in the Library Square of Columbia University, he took off his hat and raised it to the height of his arm's length to salute Miss Jennifer.

Jennifer wore a lady's hat with a veil neatly pinned to the back of her hair, and she wore a soft light gray coat with new white gloves on her hands.

"I wore gray clothes, so I put on makeup." Jennifer explained that she wore a blush that was not thick or light today.

"Uh-huh, that's good." Li Kangping approvingly.

In the United States in 1920, the use of cosmetics was no longer regarded as a label of prostitutes, and many women from good families began to wear makeup for themselves.

However, some conservative people in the United States have always been prejudiced against the makeup of good girls, so Jennifer, who wears makeup, explains why she wears makeup.

It is necessary for Li Kangping to have a clear understanding of the American culture and social customs in the 20s of the 20th century, otherwise making jokes is a trivial matter, and if it is not done well, it will cause big trouble.

Li Kangping suggested: "Jennifer, let's go to the theater district, we can watch the play after dinner, the tickets for "Laining" are sold out, but it doesn't matter, I think we can buy scalper tickets." ”

"Hey, I haven't seen you for two days, and you've already started paying attention to 'Lening,' which is a favorite of Princeton's upper class." Jennifer was fascinated, but she eventually said, "It's too late to come back from the show, you know, that old lady in our girls' dorm is nagging." ”

"Jennifer, isn't it convenient for you to go to the theater with me?"

"No, no! Lee, why do you think so? ”

"Okay, let's just eat and come back early."

Li Kangping and Jennifer took a taxi to the theater district, and the destination was a barbecue restaurant.

Not far in front of the restaurant, a crowd of people was marching, and the leader of the procession, a white man with a beard, held up a red flag, and he shouted emotionally: "What do you get out of the war?" Look around you guys and take a good look! Have you become rich? No, not really! Not only did you not get rich, but you also went bankrupt for no reason! Who else but J.P. Morgan and John D. Rockefeller reaped the benefits of the war? You're lucky to be alive and with both legs still alive! You're lucky to find out that your wife didn't run away with another man! ”

The rest of the parade roared: "To hell, blood-sucking capitalists!" ”

Suddenly, a group of American soldiers in military uniforms rushed into the procession of the marchers, and the menacing soldiers did not say a word, and directly started to do so, punching and kicking the red flag marchers.

The marchers immediately returned fire, but they were all ordinary people, and it was difficult to parry the well-trained American soldiers.

The New York police then joined the brawl, and the streets were chaotic.

Li Kangping, who witnessed all this, frowned and said: "New York is a free city, and the marchers are neither carrying guns nor bombs, why are they beating the marchers?" ”

Jennifer explained: "These marchers are Bolsheviks! And the Bolsheviks are illegal in New York, you have read the newspapers! ”

Li Kangping was extremely puzzled and said: "The United States is a democratic society with free speech. This is also written in your newspaper, and your newspaper writes it every day, isn't it? ”

"It's not democratic enough yet! Lee, do you want to stand on the street for a night? ”

"Let's go into the dining room, Jennifer."

The hilarious castanets and upbeat samba music made the ladies and gentlemen sway uncontrollably, and Jennifer fell in love with the kebab restaurant and quickly forgot about the scuffle outside.

Political arguments are not the theme of a good night out in New York, and pretty and elegant ladies and personable gentlemen should dedicate the whole night to enjoying life.

A barbecue that doesn't go well with wine has no soul. Although the menu does not include alcohol, after Mr. Lee gave the waiter $20, a bottle of rare Burgundy wine was placed on his and Jennifer's round table.

Ordinary wine costs one or two dollars a bottle, and twenty yuan wine must be a bone-eating wine.

"Looks like you're getting to know New York better." Jennifer smiled, charming and charming.

"The teacher taught well." Li Kangping picked up his wine glass.

Jennifer shook her wine glass slightly: "Mr. Li, I think your English level is fine, maybe you don't need me as an English teacher." ”

Li Kangping clinked glasses: "I don't need an English teacher, but I need friendly and smart friends to toast to friendship." ”

"Cheers."

Columbia University, an academic institution, is located in New York, a materialistic metropolis on the island of Manhattan.

Returning to Columbia's campus from the heart of Manhattan is like being in a different world.

Columbia College is a hodgepodge of colleges, which you can also understand as liberal arts colleges. Some students have been in the academy for two or even three years, they don't know which direction to major in, they study everything, and they are enrolled in many unrelated courses at the same time, such as philosophy, French literature, calculus, quantitative chemical analysis, general physics overview, history, architecture, and so on.

In the liberal arts education model, objectively speaking, some students have learned, and some students have learned.

Li Kangping's goal is clear, and he enrolled in three courses this semester: atomic theory, electromagnetism, and calculus.

After a few days of classes, Li Kangping found that some of the courses were taught by professors and some were lecturers. Of course, students are willing to enroll in professors' courses, but the number of chairs is limited, and the professors at Columbia University say a lot less, and a lot more than much.

There are several calculus teachers who are divided into several classes. The only teacher in the Atomic Theory class is Professor Rosberg, and there are currently 18 students studying the Atomic Theory in this class.

Today is Tuesday, and at six o'clock in the evening, Li Kangping came to Room 6 of the Vermont Building.

At the end of September in New York, the night was chilly. The fire in the fireplace in Room 6 was unstable, and Mr. Stephen Anderson picked up tongs and stirred the flames, pulled a log from the firewood rack and threw it into the stove.

"Mr. Jackson didn't come here and didn't ask for leave, so it seems that he is confident." Anderson is Professor Rosberg's mentor and organizes extracurricular seminars on atomic theory every Tuesday night in Room 6.

In total, more than a dozen students have registered for atomic theory, and it is clear who skipped class. Anderson is tasked with tutoring Professor Rosberg in his teaching, answering questions, solving doubts, filling gaps, and stimulating students' thinking.

"Professor Rosberg explained in a high-level summary the experiments of Ernest Rutherford's artificial nuclear reactions, which, as we know, are a new scientific achievement that has not yet had time to be included in physics textbooks. Tonight, I will explain Rutherford's experiments in detail, gentlemen, and you may interrupt me at any time. ”

Anderson draws on a small blackboard with a schematic diagram of Rutherford's artificial nuclear reaction experiment.

After drawing the diagram, Anderson tapped on the blackboard and said, "This is a closed container A, from which gas can be poured or withdrawn, and the α ray source, that is, the radium source, is placed on a stand that can be moved left and right, and the position is indicated by scale B." There is a flickering screen S not far away, and the back is observed with a microscope M. ”

A skinny, brown-haired student spoke: "Mr. Rutherford's experimental setup doesn't look amazing. ”

Anderson nodded, "Alan, you're right, Mr. Rutherford used an ordinary-looking device to get a sensational experimental conclusion. Imagine if you could design and build an experimental device with even greater energy. ”

Li Kangping replied: "Then we can break the nuclear structure of more light elements." ”

"Mr. Li wants to break more cores!" Anderson exclaimed, and he continued, "Yes, we all want to, don't we?" ”

The discussion lasted three hours, and near the end of the meeting, Anderson handed out the last assignment and then assigned the new assignment.

The last assignment was the thinking question on the binding energy of hydrogen atoms, and Li Kangping got an A, and Professor Rosberg annotated a sentence on Li Kangping's homework paper: This is the most concise and efficient algorithm I have ever seen.

The library was open until 11 o'clock in the evening, and Li Kangping borrowed a few physics journals published in 1917~1920 before closing.

It was late at night, Li Kangping poured a quarter glass of whiskey and wrote hard in the dormitory.

[Bohr, in his theory of atoms, first expressed the idea that only some of the closed orbits that can be depicted by the positively charged center of the electron are stable, while others are intrinsically impossible, or at least unstable. 】

[In order to generalize this formulation to the case of multiple degrees of freedom, Sommerfeld and Wilson proved that it is generally possible to select the appropriate coordinates qi so that they satisfy the following conditions for the quantization of the orbit: ∮pidqi=njh.] 】

[In 1917, Einstein gave a quantization condition that the form does not change with the coordinate transformation: ∮pidqi=nh.] 】①

[According to Jacobian's classical method, this integral can be converted into a full integral of the partial derivative equation: H(∂S/∂qi,qi)=W.] （i=1，2，…… f）】

[This integral has f arbitrary constants, where ......]

……

【…… In summary, all constants are deterministic. 】

【①Zum quantensatz von Sommerfeld und Epstein，Ber.der deutschen.phys.Ges.，（1917）82。 】

"The name of this assignment, I think of it, is "Analysis of Bohr-Sommerfeld Stability Conditions."

Li Kangping fought all night to complete a three-page homework.

The next morning, after the atomic theory course was over, Li Kangping walked to the podium and said, "Professor Rosberg, I have finished the homework assigned yesterday, can I hand it over to you directly?" ”

"Of course."

Professor Rothberg took a quick look at Li Kangping's assignment and looked at it, and he found that it was difficult to achieve ten lines at a glance, but he had to consider word by word.

"Analysis of Bohr-Sommerfeld stability conditions, quantum theory? Lee, I asked you to write a little paper on atomism, and you wrote about quantum theory. ”

"I'm sorry, Professor, maybe I shouldn't have done that?"

"Lee, at half past twelve at noon, you come to the second floor of the Hertley Building to find me."

"Okay, see you at noon."

Li Kangping arrived at the Hertley Building on time at half past twelve in the afternoon, and he knocked on the door of an office: "Professor Rosberg, I am Kangping Li." ”

"Lee, please come in." Professor Rosberg opened the door and welcomed Li Kangping inside.

Professor Rosberg's office is a private room, with a kettle on the stove, steaming coffee cups on the table, and an unfinished manuscript stuck in a typewriter stacked next to the typewriter with academic literature and student work.

Professor Rosberg made a gesture to sit down, and he went straight to the point: "If there is only one degree of freedom, then use the Einstein relation to determine the energy W." What if there is more than one degree of freedom? ”

Li Kangping immediately replied: "Then we can only find a relationship between W and the integer n." ”

Professor Rosberg handed him a pencil and asked, "How do you deal with the stability condition in the special case of the circular orbit of the Bohr atom?" You deal with it for me to see, right now. ”

"I'd love to do it."

Li Kangping deduced the calculation with a pen, because v=ωR, m0∮vdl=2πRm0v=nh, and continued to mathematically obtain m0ωR^2=n(h/2π).

"Professor, here's my answer."

"I believe it now, and you wrote this paper "Analysis of Bohr-Sommerfeld Stability Conditions" alone." Professor Rothberg's expression was both surprised and appreciative, and he said: "Columbia University does not include quantum theory in its undergraduate curriculum, and Tsinghua University, which is a preparatory school for studying in the United States, certainly does not offer quantum theory courses. So Mr. Li, where did you learn about quantum theory and advanced calculus skills? ”

"Professor, you know, the Columbia University Library has a complete range of academic literature, and the Tsinghua University Library also has a lot of books."

"Lord, he is self-taught!"