Shen Qi's heart sang loudly, and his subordinates moved their pens like gods:

Take the oxy as the coordinates and divide the air into many thin layers parallel to the ground.

The refractive index of the thin layer in which 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 laws of refraction and geometric relations, there are:

（dy/dx）^2=1/sin^2θ-1

After the square is opened, dy/dx takes a negative value

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

Here we want to accumulate a point, and the final integral constant C is expressed as:

C=2n1sinθ1/kαnp*arcosh（ke^α/2*H）

This is the equation for the light propagation trajectory that produces the mirage.

Through the explanation of physics and a small amount of mathematical processing, we can clearly find that the characteristic of the mirage is that "I change it and change, and finally it does not change".

If one day you are on the beach or in the desert, very lucky to encounter a mirage, do not move, just put it in place and quietly admire, in this romantic moment to confess to the girl next to you, she will gladly accept your love.

From the equation C=2n1sinθ1/kαnp*arcosh(ke^α/2*H), it can be seen that if you don't hold on and move at such a romantic moment of courtship, then the dreamlike mirage will disappear from time to time. And then the girl also ran away, everything was wooden, and the dream was shattered, what a pity.

The wonder of physics lies in the use of simple and easy-to-understand equations to explain complex and fantastic phenomena.

If physics and math join forces, this powerful technical trick will turn you into a male god.

Learn a little more knowledge, and 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 exam 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 mathematics competition, and also realized more deeply the beauty of mathematics and physics, and the two are closely related.

Physics tries to bypass complex mathematical calculations and lay the foundation for qualitative descriptions and rough quantification, but this is not possible, and the more sophisticated the field of physics, the finer the mathematical processing required. Physics is the staggering lethality of the shell, and the launch carrier determines the range, accuracy and devastating 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, bam, bam, bum, everything is possible. The best match for the math cannon is, of course, physics.

Shen Qi knows this truth very well, and contemporary mathematical gunners must be proficient in the artillery properties of various shells in order to hit a good cannon of ecstasy in various postures.

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

The semi-finals are much more difficult than the preliminary rounds, there are no multiple-choice questions, and the odds of blindness have dropped significantly.

The second question, the calculation question, is worth 16 points.

This is a quantum physics question, preliminary quantum physics.

In the CPhO competition, high school contestants only need to know some basic concepts of quantum physics and can use them simply, without having to know the principles in depth, and they do not have the ability to have an in-depth understanding. Once this thing goes deep, it's either going to win the prize, or go crazy, or go crazy.

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

All in all, this pile of emoji-like data describes a physical phenomenon: a sufficiently hot gas discharge contains a variety of ions, one of which is a nuclear charge of an atom with a Z charge that is stripped to the point that only one electron remains.

Again, there is no schematic diagram, Shen Qi needs to find some useful clues from the large amount of data on the question, and finally find the value of Z, and write out what kind of element ion it is.

In the physics problems of mechanics, acoustics, and electromagnetism of physical competition, the schematic diagram often contains a lot of information that can be used, and reading the diagram is an important step in the examination of the problem. Quantum physics is different from them, there is not much difference between giving a graph or not, and most of the work depends on the answerer's own brain.

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

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

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

The beginning of the semi-final is a two-headed roadblock, and the second question is not easy.

First of all, Shen Qi needed to find inspiration from Heisenberg.

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

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

Historically, there is controversy about Heisenberg, who conducted research for the Nazis during World War II and researched the atomic bomb. Of course, it was the Americans who were the first to develop the atomic bomb and use it in actual combat.

Heisenberg's political orientation aside, the "Heisenberg Uncertainty Theory" he proposed has a high status in the academic community.

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

With a little processing in this state, the average value of the square value of the distance from the electron to the center of the nucleus is r0^2.

It's not complicated math.

High school students who participate in the semi-finals only need to know that r0^2 is defined as the sum of the squares of the uncertain quantities of position coordinates (△x)^2, (△y)^2, and (△z)^2.

The requirement for a good high school candidate is to be able to apply the "Heisenberg Uncertainty Principle" in a simple way, without having to understand it in depth. Understand that it is the business of college students, and talk about it later.

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

A^(Z-1)+ ions capture an electron and emit a photon, and this process must observe the conservation of energy and momentum.

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

By Heisenberg's uncertainty principle:

（△x）（△px）≥1/2 ћ

（△y）（△py）≥1/2 ћ

（△z）（△pz）≥1/2 ћ

The equation for conservation of energy can be specifically expressed as:

1/2meve^2+1/2(M+me)v^2+E off = 1/2 (M+2me)μ^2+E' off + ћω0

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

To(∩_∩)To���������......���(╥_╥)��

(The above formula is displayed in word is garbled, brain make up it, the author can't do anything)

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

Mathematicians and physicists don't need to express their thoughts in any written language, they throw out a bunch of symbols when they don't agree with each other, read for themselves, and then speak after they understand.

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 silently counted in his heart, hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine, neon, ......