I just want to be a quiet scholar

Chapter 89 Optics and Quantum Theory
Shen Qi's heart sang in his heart, and his brush was like a god:
Take oxy as the coordinates and divide the air into many thin layers parallel to the ground.

The refractive index of the thin layer where the object point P is located is n1.

The angle between the ray and the ground normal is θ1.

The following layers are n2, θ2, n3, θ3...

According to the law of refraction and geometric relationship, there are:
(dy/dx)^2=1/sin^2θ-1
After squaring, dy/dx takes a negative value

故：dx=-2n1/kαnp*sinθ1*dφ/（φ^2-1）^1/2
Here to integrate a point, the final integration constant C is expressed as:
C=2n1sinθ1/kαnp*arcosh(ke^α/2*H)

This is the ray propagation trajectory equation that produces the mirage.

Through the explanation of physics and a small amount of mathematical processing, we can clearly find that the mirage is characterized by "I change it and it changes, and eventually it disappears".

If one day you are at the seaside or in the desert, you are very lucky to encounter a mirage, don't move, just leave it in place and enjoy it quietly, and confess to the girl around you at this romantic moment, she will definitely accept your love.

From the light propagation trajectory equation C=2n1sinθ1/kαnp*arcosh (ke^α/2*H), we can see that if you don’t hold and move during such a romantic courtship moment, then the mirage like a dream will disappear and appear in the end. Disappear.Then the girl also ran away, there was nothing left, the dream was shattered, what a pity.

The magic of physics is that it uses simple and easy-to-understand equations to explain complex and dreamy phenomena.

If physics and math join forces, this powerful technique of pickup will turn you into a male god.

Learn a little more, and one day it will come in handy.

When you reach the pinnacle of human knowledge, hehe... Shen Qi smiled, he wrote the answer on the test paper: C=2n1sinθ1/kαnp*arcosh(ke^α/2*H)

After completing the first fill-in-the-blank question, Shen Qi got a little bit of the passion of last year's math competition, and also more deeply realized that mathematics and physics have their own beauty, and the two are closely related.

Physics tries to circumvent complicated mathematical calculations and make a breakthrough with qualitative description and rough quantification, but this is impossible. The more sophisticated the field of physics is, the more refined the mathematical processing required.Physics is an amazingly lethal projectile, and the launch vehicle determines the range, accuracy and destructiveness of the strike.

Mathematics mostly stays on paper and in the minds of mathematicians. It is like an infinitely powerful cannon, except that there are no shells in the chamber.Once the shells are filled, bang!Boom!Everything is possible.The best match for the math cannon is, of course, physics.

Shen Qi is well aware of this truth. Contemporary math gunners must be proficient in the artillery properties of various cannonballs in order to shoot ecstasy good cannons in various postures.

The first question of the CPhO rematch is a fill-in-the-blank question, and the next seven questions are all calculation questions.

The rematch was much more difficult than the preliminary round. There were no multiple-choice questions, and the chance of being blindfolded dropped significantly.

The second question, calculation question, 16 points.

This is a quantum physics question, preliminary quantum physics.

In the CPhO competition, high school players only need to know some basic concepts of quantum physics and can simply use them.Once this thing goes deep, it will either win the prize, or go crazy, or win the prize in a crazy state.

The title gives a bunch of data and constants, electron charge, electron mass, Bohr radius, Rydberg energy, proton static energy...

All in all, this emoji-like set of data describes a physical phenomenon: A sufficiently hot gas discharge contains various ions, one of which is an atom with a nuclear charge of Z stripped away to just one electron.

There is also no schematic diagram. Shen Qi needs to find some useful clues from the large amount of data on the topic, and finally find the value of Z and write out what element ion is this.

In the physical problems of mechanics, acoustics, and electromagnetism of the competition, the schematic diagram often contains a lot of information that can be used. Reading the diagram is an important step in reviewing the problem.Quantum physics is different from them. It doesn't make much difference whether to give a picture or not. Most of the work depends on the answerer's own brain.

There are many brain-burning branches of physics, of which TOP5 must have a place in quantum physics.

From macroscopic optical refraction to microscopic ion trapping, from mirage to electronic ground state, there is little connection.

Physics contains too many things, so Shen Qi switched to quantum mode and began to solve the 16-point calculation problem.

The start of the rematch is a roadblock at both ends, and the second question is not easy.

First, Shen Qi needed to find inspiration from Heisenberg.

Heisenberg is not a place name, he was a prominent German physicist, second only to Einstein in his contribution to quantum theory.

Heisenberg was a genius, even a physics genius, winning the Nobel Prize in Physics at the age of 31.When Einstein won the Nobel Prize in Physics, he was no longer confused.

Historically, the evaluation of Heisenberg was controversial. He engaged in scientific research for the German government during World War II and studied the atomic bomb.Of course, it was the Americans who first came up with the atomic bomb and used it in actual combat.

Aside from Heisenberg's political orientation, his "Heisenberg Uncertainty Principle" has a high status in academia.

Shen Qi first used the "Heisenberg Uncertainty Principle" to make a surprise attack, and set the only electron in A^(Z-1)+ to be in the ground state.

A little processing in this state can obtain the average value of the square value of the distance from the electron to the nucleus center r0^2.

This is an uncomplicated mathematical operation.

参加物竞复赛的高中生只需知道，r0^2定义为位置坐标不确定量平方（△x）^2、（△y）^2、（△z）^2之和即可。

The requirement of a good high school physical game player is to be able to simply apply the "Heisenberg Uncertainty Principle" without having to understand it in depth.It's a college student's business to gain a deep understanding, and we'll talk about that later.

According to the gourd and the scoop, Shen Qi obtained the average value of the square of the electron momentum p0^2 in this state.

The A^(Z-1)+ ion captures an electron and emits a photon. This process must obey the conservation of energy and momentum.

Both conservation relations contain the angular frequency ω0 of the emitted photon, and they form a system of equations containing ω0.

By Heisenberg's uncertainty principle:
(△x) (△px)≥1/2
(△y) (△py)≥1/2
(△z) (△pz)≥1/2
The energy conservation equation can be specifically expressed as:

1/2meve^2+1/2(M+me)v^2+E离=1/2(M+2me)μ^2+E’离+ω0
Next, a wave of slightly complicated mathematical operations needs to be implemented, which is not difficult for Shen Qi:

O(∩_∩)Omeowo(╥﹏╥)o…

(The above formula is displayed as garbled characters in word, so make up for it, the author is powerless)
To a certain extent, mathematics and physics research are not much different from metaphysics in the eyes of outsiders.

Mathematicians and physicists do not need to express their thoughts in any written language. When they disagree, they throw out a bunch of symbols. Look at it for yourself, and let’s talk when you understand it.

After a series of calculations, Shen Qi finally got the value of Z.

Z = 4
"This... Z is equal to 4." Shen Qi thought for a while and counted in his heart, hydrogen helium lithium beryllium boron, carbon nitrogen oxygen fluorine neon...

(End of this chapter)