Teacher Xu, Please Take Care of the Reckless Students in Your Class

As for the last question, Li Jing took a deep breath, "According to previous exams, this last question is the most difficult, and it must be the final question!"

"In previous years, I didn't have enough time, but this year is different. I have more than two hours, and I still can't take this question."

He is mentally prepared!

Read the question carefully.

Zeeman discovered that the sodium D-line splits into three in a magnetic field, which Lorentz explained based on classical electromagnetic theory, for which they were awarded the 1902 Nobel Prize in Physics.

Assume that the valence electrons in the atom (mass m, charge -e, e>0) are acted on by an equivalent linear restoring force -mw0^2r (r is the potential vector of the valence electrons relative to the atomic center) towards the center of the atom , do simple harmonic vibration with natural circular frequency w0, and emit light with circular frequency w0.

Now place the atom in a uniform magnetic field along the positive direction of the z-axis, and the magnitude of the magnetic induction is B (for convenience, B is parameterized as B=(2m/e)*wL).

(1) Choose a reference frame that rotates at a constant angular velocity around the magnetic field, make the valence electrons perform simple harmonic vibration in the reference frame, derive the component form of the dynamic equation of the electron motion in the Cartesian coordinate system and find its solution ;

(2) Transform the component form of the solution in (1) in the rectangular coordinate system to the rectangular coordinate system of the laboratory reference system;

(3) Prove that the spectral line with circular frequency ?0 emitted by atoms in the laboratory reference frame is divided into three parts in the magnetic field; for the case of weak magnetic field (ie wL<<w0), find the frequency interval of the three spectral lines .

It is known that in the rotating reference frame with the rotational angular velocity w, the inertial force on the moving electrons is also affected by the Coriolis force in addition to the inertial centrifugal force. The Coriolis force is fc=-2mw*v'.

Li Jingyi muttered, "It doesn't seem to be as difficult as I imagined. Could it be my personal reason? Or is it that the topics in this volume are not that difficult."

He tried to get started.

"The laboratory reference frame Oxyz with the positive ion center as the origin O and the reference frame Ox'y'z' rotating around the z-axis with the angular velocity w..."

He drew a picture.

"The z-axis and z'-axis coincide, along the direction of the magnetic field."

"Remember the coordinate axes of the two reference systems? The positive unit vectors are i, j, k and i', j', k' respectively."

"In a rotating system, in addition to the linear restoring force -mx0^2r and Lorentz force -ev*B, valence electrons are also affected by inertial centrifugal force -mw*(w*r) and Coriolis force -2mw*v , the combined force of which is…”

Li Jingyi wrote on the acting paper.

At this time, his mentality was the same as the previous question.

Try to write first, have some ideas.

Play on the papyrus:

F'=-mw0^2r-ev*B-mw*(w*r)-2mw*v

Li Jingyi muttered, "If it is written in the form of equivalent weights...then this..."

As he wrote and wrote, Li Jingyi used up two pieces of acting paper.

This question does not look simple, but it requires a lot of computation, and it also uses the dynamic equation of electron motion, the amplitude vector method, and other knowledge points.

Li Jingyi keeps using braces!

There are three calculation formulas involved in each curly bracket, and there are various parentheses and curly brackets in these three formulas, and the amount of calculation is huge!

But in the end, Li Jing got the answer.

"Huh... just came out like this?"

For a while, Li Jingyi was a little surprised.

Maybe it was a coincidence that he could get the answer to the last question, but it was the same for the second time, and this question was the final question, which made him a little suspicious.

Li Jingyi's eyes twitched, and he immediately looked back at his playing paper.

From the formula in the first line, it is almost a word.

"That's right...that's right here..."

After reading it for the first time, Li Jingyi wondered, "That's right! Is it really that the question is too simple?"

Doubt.

squeak-

There was a sound of the bench being pushed away in the examination room.

Li Jingyi raised his head suddenly, only to see Wei Minghai and He Ruohua getting up almost at the same time and handing in the papers!

It's only been an hour!

In one hour, I did five questions!

Li Jingyi lowered his head suddenly, he suddenly had an idea in his mind, it wasn't him who made the question, but the question was too easy for them!

The three invigilators in the examination room were instantly stunned!

"You, are you...?"

Wei Minghai, "Delivery."

He Ruohua also smiled, "Hand in."

Immediately after, the two looked at each other, laughed, packed their things, and walked out of the examination room.

the entire examination room.

The three invigilators and all the candidates were stunned.