Xueba starts with change

Chapter 564 The Significance of Doing Research
It was late at night, but Chen Zhou was still immersed in his own research.

At this time, Chen Zhou came back again, deriving the formula of neutrino oscillation probability.

"In general, considering the average momentum of neutrinos p>>m1, m2..."

"Combining the average energy E of the neutrino beam, the distance l between the neutrino generation point and the detection point, and the oscillation length L..."

“就可以得到中微子束能量之间的关系式，即(E1-E2)t≈(m1-m2）t/2p=Δmt/2p=1/2Δml/E=2πl/L……”

Without even thinking about it, Chen Zhou wrote out this relational formula on the draft paper.

This is his second derivation tonight.

After writing this relational expression, Chen Zhou glanced at it, and then substituted this relational expression into the formula of the probability P(Ve→Vμ, t) of Vμ.

On the draft paper, the derivation of the formula also continued to the next step.

【代入Vμ的概率大小P(Ve→Vμ，t)后，就会有P(Ve→Vμ，t)=1/2sin2θ[1-cos(2.54Δml/E)]=sin2θsin(1.27Δml/E)】

【Therefore, P(Ve→Ve, t)=1-sin2θsin(1.27Δml/E)...】

The establishment of this relationship is actually based on the phenomenon of neutrino oscillation.

The relational formula also shows that after a beam of pure electron neutrinos passes through a certain distance, part of them will be transformed into muon neutrinos.

The condition is that θ and Δm are not zero.

As long as these two parameters are not zero, neutrinos of different flavors can transform into each other, resulting in neutrino oscillation.

At the same time, this point also shows that if the existence of neutrino oscillation is confirmed in the laboratory.

It can be deduced that there is at least one kind of neutrinos whose mass is not zero.

Of course, Chen Zhou didn't think too much about it now, there are issues about neutrino mass and neutrino oscillation.

In other words, his current focus has shifted from neutrino oscillation to the new formula.

After writing this relational expression, Chen Zhou hardly stopped, so he extended this relational expression to the mixture of three neutrino flavors.

[The connection between flavor eigenstates and quality eigenstates can be expressed as...]

[By rotating the transformation matrix, the relational expression can be further rewritten as a matrix represented by three Euler angles θ3, θ12, θ23 parameters...]

[For the neutrino oscillation probability, there is also P(Vα→Vβ, t)=∣i=1→N∑Uαie^(-iEit)Uiβ∣……】

Although on the draft paper, the expression of the oscillation probability P written by Chen Zhou is extremely complicated.

However, Chen Zhou's heart became clearer.

Following the derivation formula along the way, Chen Zhou once again deduced the expression of the oscillation probability P to the new formula he discovered.

However, the method used by Chen Zhou this time is somewhat different.

When Chen Zhou discovered this new formula for the first time, he did not use a purely mathematical method.

Later, although because of the strong feeling, Chen Zhou repeated the deduction.

However, Chen Zhou still made a certain connection between it and the subject of neutrino oscillation.

No, it is regarded as a purely mathematical problem and is being studied.

Moreover, when Chen Zhou was proving, he was more concerned with the Hermitian matrix.

But the Hermitian matrix has an important property, that is, its eigenvalues ​​must be real numbers!
This happens to match quantum mechanics, or the situation in physics.

Because in quantum mechanics, the eigenvalues ​​of a matrix often correspond to a real physical quantity.

For example, energy, number of particles, and so on.

In physics, there are many situations where Hermitian matrices are used.

Chen Zhou discovered the new formula because he was studying neutrino oscillation related topics.

Naturally, he was also limited in this regard.

In the process of initially proving the new formula, Chen Zhou used a 3×3 Hermitian matrix.

From this particular case, a more general conclusion is then deduced.

If you can jump out of physics, the situation of non-Hermitian matrices is more common.

If the new formula cannot be used in other situations, its usefulness will be greatly reduced.

Although the proof process given by Chen Zhou is not entirely confined to the Hermitian matrix.

But compared with the more general situation, the proof given by Chen Zhou is still not enough.

Fortunately, Chen Zhou conducted a more in-depth derivation and research on the formula of neutrino oscillation probability.

Chen Zhou gradually figured out what was the cause of the sudden strong feeling before.

After Chen Zhou figured out the reason, there was room for improvement.

This time, Chen Zhou intends to completely skip the subject of neutrino oscillation.

Purely from a mathematical point of view, use basic mathematical methods to prove this new formula.

As time passed, the night deepened.

But at this moment, Chen Zhou was full of energy.

"If you use the proof method of Kramer's rule, you should be able to extend the formula to the case of non-Hermitian matrices..."

"But why do I always feel that this formula has limited significance in numerical calculations..."

"Even if it is extended to the general situation, how to verify the sign of each component of the eigenvector is still a problem..."

Looking at the formulas and mathematical symbols on the draft paper, Chen Zhou habitually tapped the draft paper with a pen.

Suddenly, Chen Zhou took all the draft paper in front of him to one side, and took out a brand new A4 draft paper.

Start writing and checking on it.

Chen Zhou discovered the core of the problem.

That is, this formula cannot be solved through examples.

We have to change our way of thinking, change our perspective.

Otherwise, the scope of application of this formula will be limited to death.

Chen Zhou discovered that the essence of this new formula method is to use the eigenvalues ​​of the original Hermitian matrix and the eigenvalues ​​of the sub-matrix to work together to calculate the possible eigenvectors of the original Hermitian matrix.

Therefore, it still needs the information of the original Hermitian matrix in it.

If all eigenvectors need to be calculated, all submatrices are needed.

Due to the similarity transformation of Hermitian matrices, both are possible eigenvectors.

However, this calculation method lacks phase information in it.

Therefore, the calculated eigenvector is not unique.

What's more, if you don't know the information of the original Hermitian matrix, it is meaningless.

But in fact, for many physical problems, it may not be possible to obtain the full original Hermitian matrix.

Only some specific physical problems can use this new formula to reduce the calculation intensity.

But this amount of calculation has not actually been reduced much.

Of course, the application of this new formula in the field of neutrinos is quite valuable.

It's a pity that Chen Zhou doesn't want such a new formula to be limited to only one research field.

Chen Zhou hopes that this new formula can really be "new".

What Chen Zhou needs to do now is to conduct further in-depth research on this new formula.

It has universal practical value and can be expanded in other fields.

Moonset and sunrise.

Chen Zhou once again spent the whole night in front of the desk.

Rubbing his eyes, Chen Zhou felt a little tired.

This high-intensity research to maintain his mental state still made him feel a little tired.

Especially in the research process, coupled with the reading of a large number of literature.

It really made Chen Zhou a little overwhelmed.

That's right, Chen Zhou also consumed a lot of the documents that Chen Zhou downloaded earlier in the process of research.

But fortunately, the results of liver explosion research still satisfied Chen Zhou.

He is still a little short of his goal.

Moreover, Chen Zhou is confident that the problems left by this new formula can be solved today.

To say that the only thing that Chen Zhou is not happy about is that when he was looking through the literature, he discovered some "new problems" of this new formula.

This "new question" also lowered Chen Zhou's original sense of expectation a lot.

Chen Zhou discovered that although this new formula was discovered by his independent research, he was not the first to create it.

As early as 2014, this new formula was discovered by a Dutch scholar.

Moreover, the prototype of this formula can even be traced back to 1968...

That is to say, what Chen Zhou originally thought, the situation that other physicists could not take the lead will never happen again.

He is a latecomer.

When he first discovered this new problem, Chen Zhou even wondered if he was dazzled?

After reading it repeatedly, Chen Zhou confirmed the tragic news.

At this time, Chen Zhou, who originally had only one way, now has two choices.

One is to give up the in-depth study of the new formula, and leave this formula discovered halfway.

The other is, regardless of the right to discover this new formula, the research will continue in depth.

A simple formula, just like Chen Zhou's strong feeling, has a limited scope of application.

When it cannot be applied to general situations, its value is only that.

Only by doing more in-depth research and unlocking the shackles of this formula, can it have greater value and play a greater role.

But in this case, it feels like making a wedding dress for the discoverer of this formula.

Because when people mentioned this formula later, when it came to the discoverer of this formula, it was not Chen Zhou.

This is also what Chen Zhou is most upset about.

He didn't want to choose either of these two options.

He still remembers the excitement on his face when he first discovered this new formula.

It's a pity, it's all too late...

After reading the document that made Chen Zhou feel uncomfortable again, Chen Zhou finally chose to ignore this document.

After adjusting his mentality a little, he devoted himself to the research of the new formula again.

After all, he, who is immersed in the research of the new formula, actually does not want to give up this research from the bottom of his heart.

Even if people talk about this new formula in the future, the name of the discoverer is not him, so what?

As long as people remember that it was he who maximized the value of this new formula, it was worth it.

In the process of scientific exploration, the thing of "reinventing the wheel" has never been new.

The most famous, like Newton and Leibniz, independently invented calculus.

In the computer field, there are also Turing and Church, who successively proposed the general computer theory.

Chen Zhou feels that such things have happened before, and will happen in the future.

And like him, people who conduct research in multidisciplinary fields are even more likely to meet.

What he can and should do is to maintain the mentality of a scholar.

From an academic point of view, do your own academic research with the greatest ability.

Just like those who make outstanding achievements and advance the development of disciplines in every field.

Although they are not the original discoverers, who can say that they are not masters?
And this is what research is all about!
With this belief in mind, Chen Zhou maintained the best mental state and continued the research on the new formula.

Only after this night of explosive liver research did he come close to the goal.

……

Getting up and walking to the window, Chen Zhou took a few breaths of fresh air, and then went to wash up.

Then go out to solve breakfast.

People are iron rice is steel.

Occasionally bursting into research and staying up late, Chen Zhou didn't feel anything.

But from last night to now, he still couldn't bear it because he hadn't eaten.

What Chen Zhou pursues is that it is okay to waste sleep, but not to forget food.

After finishing breakfast, Chen Zhou returned to his room and began to sleep for a while.

He planned to rest for two to three hours before getting up and finishing the rest of the research.

If he dragged his tired body to study again, Chen Zhou worried that it would be counterproductive.

Three hours passed quickly.

Chen Zhou was also woken up by the alarm clock set.

He rubbed his hazy eyes, turned over and got out of bed.

After simply washing his face, Chen Zhou sat down at the desk again.

After glancing at the draft paper on the desk that hadn't been sorted out yet.

On a whim, Chen Zhou did eye exercises.

After a set of eye exercises was over, Chen Zhou's mental state also completely woke up from the hazy state of just waking up.

Turning on the computer, Chen Zhou flipped through the previously downloaded documents and the documents downloaded last night.

While starting to invest in the final research of the new formula.

After screening and reviewing these documents, Chen Zhou found that although this new formula was indeed discovered by others, it was discovered a long time ago.

However, no one has made substantial research progress in the in-depth study and extended application of the new formula.

In other words, his research is ahead of everyone at this moment.

After confirming this, Chen Zhou's mood also improved.

As long as Chen Zhou brings out the universal value of this new formula.

A discoverer, then, will never be remembered alone.

Even scholars in more fields will thank Chen Zhou.

The pen in Chen Zhou's hand kept leaving mathematical symbols one after another on the brand new A4 draft paper.

With the emergence of mathematical symbols one after another, Chen Zhou's research on new formulas has become more and more in-depth.

The so-called general situation is actually the most general applicability.

To achieve the most general applicability, it is necessary to take into account all circumstances.

As a new formula for basic mathematics, it needs to be considered enough.

The current Chen Zhou is very conscious of this.

Finally, after verifying his own research results from one angle after another.

Chen Zhou solved the general situation of the new formula and confirmed the general applicability of the new formula.

In other words, the new formula now will really enable people to calculate the eigenvectors using only the eigenvalue information!
Chen Zhou went a step further and revealed new facts about basic mathematics!

Future new formulas will not only be limited to Hermitian matrices.

It's not just for the neutrino problem, either.

It will play its application value in mathematics, physics, engineering and other disciplines!
　Thanks to book friend cwjxqb for rewarding 1500 starting coins!
　　Thank you book friend Ning Ningzi for the 138 starting coins!
　　Thanks to book friend Yan Hongxue for the 100 starting coins!
　　
　
(End of this chapter)