I Just Want to Be a Quiet Top Student

A singing voice sounded in Shen Qi's heart, and he moved his brush like a god:

Take oxy as the coordinate, 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 light and the ground normal is θ1.

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

According to the law of refraction and geometric relations, there are:

(dy/dx)^2=1/sin^2θ-1

After square root, dy/dx takes a negative value

Therefore: dx=-2n1/kαnp*sinθ1*dφ/(φ^2-1)^1/2

One point is to be accumulated here, and the final integral constant C is expressed as:

C=2n1sinθ1/kαnp*arcosh(ke^α/2*H)

This is the light 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 characteristic of mirage is "I change it and it changes, and finally it disappears".

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

According to the light propagation trajectory equation C=2n1sinθ1/kαnp*arcosh (ke^α/2*H), if you do not hold and move during such a romantic courtship moment, then the mirage like a dream will appear and disappear from time to time, and finally Disappear. Then the girl also ran away, nothing was left, and the dream was shattered, what a pity.

The wonder of physics lies in the interpretation of complex and dreamy phenomena with simple and easy-to-understand equations.

If physics and math join forces, this powerful technical pull-up method will turn you into a male god.

Learn more knowledge, it will come in handy one day.

When you reach the pinnacle of human knowledge, hehe... Shen Qi smiled, and 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 deeply realized that mathematics and physics have their own beauty, and the two are closely related.

Physics tries to circumvent complex mathematical calculations and establish a world with qualitative description and rough quantification, but this is impossible. The more sophisticated the field of physics, the more sophisticated the mathematical processing required. Physics is a cannonball with amazing lethality, and the launch carrier determines the range, strike accuracy and destructiveness.

Mathematics stays on paper and in the minds of mathematicians most of the time. It is like a powerful cannon, but there are no shells in the chamber. Once the cannonball is loaded, bang! bang bang! Everything is possible. The shell that best matches the mathematical cannon is, of course, physics.

Shen Qi is well aware of this truth. Contemporary mathematical gunners must be proficient in the artillery properties of various shells in order to shoot ecstasy with various postures.

The first question in the CPhO rematch is to fill in the blanks, and the next seven questions are calculation questions.

The rematch is much more difficult than the preliminary round, and there are no multiple-choice questions, so the chance of getting confused is greatly reduced.

The second question, calculation question, 16 points.

This is a quantum physics problem, elementary quantum physics.

In the CPhO competition, high school contestants only need to know some basic concepts of quantum physics, and can use them simply. They don't need to understand the principles in depth, and they don't have the ability to understand them in depth. Once this thing goes deep, you 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 bunch of emoticon-like data describes a physical phenomenon: a hot enough gas discharge will contain various ions, one of which is an atom with a nuclear charge of Z that is stripped to only one electron.

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

In the physics problems of mechanics, acoustics, and electromagnetism of Wujing, the schematic diagram often contains a lot of information that can be used, and reading the picture is an important step in reviewing the problem. Quantum physics is different from them. There is no big difference between giving pictures or not. Most of the work is done by the answerers themselves.

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

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

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

At the beginning of the rematch, there were two obstacles in the way, and the second question was not easy.

First, Shen Qi needs to find inspiration from Heisenberg.

Heisenberg is not a place name. He is an outstanding physicist in Germany, and his contribution to quantum theory is second only to Einstein.

Heisenberg is a personal talent and can even be said to be a physical genius. He won the Nobel Prize in Physics at the age of 31. Einstein was in his prime when he won the Nobel Prize in Physics.

Historically, the evaluation of Heisenberg has been controversial. During World War II, he conducted scientific research for the German government and studied the atomic bomb. Of course, the Americans were the first to develop the atomic bomb and use it in actual combat.

Regardless of Heisenberg's political orientation, the "Heisenberg Uncertainty Principle" he proposed has a high status in academia.

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

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

This is an uncomplicated mathematical operation.

High school students participating in the physical competition rematch only need to know that r0^2 is defined as the sum of the squares of the position coordinate uncertainty (△x)^2, (△y)^2, (△z)^2.

The requirement for an excellent high school biology contestant is to be able to simply use the "Heisenberg Uncertainty Principle" without in-depth understanding. Deeply understand that it is the business of college students, let's talk about it later.

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

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

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

According to the Heisenberg 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+Eli=1/2(M+2me)μ^2+E'li+ω0

Next, a wave of slightly complicated mathematical operations needs to be implemented, which is not difficult for Shen Qi:

O(∩_∩)O喵o(╥﹏╥)o...

(The above formula is displayed as garbled characters in word, let’s make it up, the author can’t do anything)

To a certain extent, mathematics and physics research are not much different from metaphysics in the eyes of outsiders.

Mathematicians and physicists don't need to use any language to express their ideas. They just throw out a bunch of symbols when they disagree. Let's see for ourselves. Let's talk after we understand.

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

Z=4

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