It was already late at night, but Chen Zhou was still immersed in his research.

At this time, Chen Zhou returned again and deduced the formula for the probability of neutrino oscillation.

"Generally speaking, considering the average momentum of neutrinos pm1, m2..."

"If combined with 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..."

"You can obtain the relationship between the energy of neutrino beams, that is, (E1-E2)t≈(m12-m22)t/2p=Δm2t/2p=1/2Δm2l/E=2πl/L..."

Chen Zhou didn't even think about it and wrote this relationship on the draft paper.

This is his second deduction tonight.

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

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

[After substituting the probability size of Vμ P(Ve→Vμ,t), P(Ve→Vμ,t)=1/2sin22θ[1-cos(2.54Δm2l/E)]=sin22θsin2(1.27Δm2l/E)]]

【So, P(Ve→Ve,t)=1-sin22θsin2(1.27Δm2l/E)…】

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

The relationship also shows that after a bunch of pure electron neutrinos passes through a certain distance, part of them will be converted into muon neutrinos.

The condition is that θ and Δm2 are not zero.

As long as these two parameters are not zero, neutrinos with different flavors can be converted to each other to produce neutrino oscillation.

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

It can be concluded that at least one type of neutrino has a mass not zero.

Of course, Chen Zhou has not thought too much now, and there are questions about neutrino mass and neutrino oscillation.

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

After writing this relationship, Chen Zhou almost stopped and promoted this relationship to a mixture of three neutrino flavors.

[The connection between the taste eigenstate and the mass eigenstate can be expressed as...]

[By rotating the transformation matrix, the relationship can be further rewritten into a matrix represented by the three Euler angles θ12, θ23, θ13 parameters...]

[For the probability of neutrino oscillation, there is also P(Vα→Vβ,t)=∣i=1→N∑Uαie^(-iEit)Uiβ?∣2…]

Although the expression of the oscillation probability P written by Chen Zhou on the draft paper 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 on the new formula he discovered.

However, the methods used by Chen Zhou this time are a little different.

When Chen Zhou first discovered this new formula, he did not use pure mathematical methods.

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

However, Chen Zhou still made some connections with the topic of neutrino oscillation.

Not, considering it as a purely mathematical problem, researching it.

Moreover, when Chen Zhou proved, he made more proofs for the Hermi matrix.

However, the Hermi matrix has an important property, that is, its eigenvalue must be real numbers!

This point matches the situation in quantum mechanics, or physics.

Because in quantum mechanics, the eigenvalue of a matrix often corresponds to a real physical quantity.

For example, energy, particle count, etc.

In physics, there are many cases where the Hermi matrix is ​​used.

The reason why Chen Zhou discovered the new formula is because he was studying related topics of neutrino oscillation.

Naturally, he was also subject to this limitation.

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

Then, from this special situation, a more general conclusion is inferred.

If you can go beyond physics, the non-Hermi matrix situation is more common.

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

Although the proof process given by Chen Zhou is not limited to the entire Hemi matrix.

However, compared with the more general situation, the proof given by Chen Zhou is still insufficient.

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

Chen Zhou gradually figured out what was the sudden and strong feeling that had suddenly appeared before.

Chen Zhou, who has figured out the reason, has room for improvement.

This time, Chen Zhou planned to completely break out of the neutrino oscillation issue.

Simply prove this new formula from a mathematical perspective and basic mathematical methods.

As time goes by, the night is deepening.

But at this moment, Chen Zhou had a full spirit.

"If you use the proof method of Kramer's law, you should be able to extend the formula to a non-Hermi matrix case..."

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

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

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

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

Start writing and verifying it.

Chen Zhou discovered the core of the problem.

That is, this formula cannot be solved by the method of universal examples.

We must change our thinking and perspective.

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

Chen Zhou discovered that the essence of this new formula method is actually to use the eigenvalue of the original Hermi matrix and the eigenvalue of the sub-matrix to calculate the possible eigenvectors of the original Hermi matrix.

Therefore, it actually requires the information of the original Hermi matrix.

If all eigenvectors need to be calculated, all submatrixes are required.

Because of the similar transformation of the Hermi matrix, all are possible eigenvectors.

This method of calculation lacks phase information inside.

Therefore, the calculated intrinsic arrows are not unique.

What's more, it would be meaningless if you don't know the information of the original Hermi matrix.

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

There are only some specific physical problems that can be used to reduce the calculation intensity through this new formula.

But this calculation volume has not been reduced much.

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

Unfortunately, Chen Zhou did not want such a new formula to be limited to one research field.

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

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

Make it have universal practical value and can be expanded in other fields.

Moonset and sunrise.

Chen Zhou spent the whole night at his desk again.

After rubbing his eyes, Chen Zhou felt a little tired.

This high-intensity study of maintaining his mental state still made him feel a little tired.

Especially during the research process, a large amount of literature is read.

It really made Chen Zhou unable to withstand it.

That's right, Chen Zhou's previous downloaded literature was also consumed by Chen Zhou during the research process.

Fortunately, the results of the liver-burning research still satisfies Chen Zhou.

He is still a little short of his goal.

And Chen Zhou is confident that he can solve the problems left over from this new formula today.

The only thing that Chen Zhou was unhappy was that when he was flipping through the literature, he discovered some "new problems" of this new formula.
To be continued...