Xueba starts with change

Chapter 632 Classes Are Also a Source of Inspiration

Chen Zhou didn't know why, but he suddenly felt something.

It may also be due to research.

After all, during this period of research, the focus was on gauge field theory and the Yang-Mills equation.

Moreover, the combing of a large number of documents made Chen Zhou want to sort out as long as he saw something he was interested in.

Therefore, when Chen Zhou saw the part of the textbook about the relationship between conserved quantities and symmetry.

I just want to start with the most basic content in the textbook.

While giving lessons to the students, I also review it myself.

"Compared with classical mechanics, the study of symmetry in quantum mechanics starts from the system. Let the state of the system be φ, and the evolution of φ follows the Schrödinger equation ih/t(φ)=Hφ..."

"Considering a certain linear transformation Q, this Q has an inverse transformation Q-1, which does not depend on time, then φ→φ'=Qφ, which also shows that the system is invariant to the transformation, as φ' and φ follow the same form The equation of motion, φ' also obeys the Schrödinger equation..."

Chen Zhou on the stage began to explain the symmetry in quantum mechanics by combining the Schrödinger equation.

For the students in the audience, this is naturally what they hope to see.

They became even more excited when they found out that Chen Zhou started to conduct extended teaching in combination with textbooks.

They did not expect that the students of the Department of Mathematics in the morning had only one happiness of distribution deconstruction.

When I came to them, I actually came twice.

Is this double happiness?
At the same time, the students of the physics department secretly decided that if anyone said that Professor Chen Zhou was a fake physicist but actually a mathematician, then they would definitely not let him go!

Isn't such an obvious preference enough to prove that Professor Chen Zhou is actually a fake mathematician and a real physicist?
Chen Zhou naturally didn't know what these students were thinking, and he was still explaining the relationship between conserved quantities and symmetry carefully.

However, with the passage of time, Chen Zhou's lecture pattern and rhythm began to change.

The speed of Chen Zhou's explanation began to become faster and faster.

And the depth of this part of the content also began to slide deeper...

This point can also be seen from the frowning of many students.

The reason they frowned was precisely because of the depth of Chen Zhou's explanations, which sounded a bit difficult to them.

They could only do their best to take notes of what Chen Zhou explained.

Wait until afterwards, and then spend time on your own to repeat the study.

In contrast to Chen Zhou's words, if you observe carefully, you will find out.

At this moment, Chen Zhou's eyes became brighter.

The expression on his face also changed slightly.

Just because he discovered that this part of the superficial content about the relationship between conserved quantities and symmetry unexpectedly inspired him...

This surprise, to Chen Zhou, can be said to be quite a surprise.

He really never thought that he could get inspiration for his own project through the course content of undergraduates.

He never thought that giving lessons to students would also be a source of inspiration...

But no matter what, the surprise of the inspiration made Chen Zhou feel very good.

"The space-time symmetry of a mechanical system is the invariance of its law of motion. In quantum mechanics, the law of motion is the Schrödinger equation. The Schrödinger equation determines the Hamiltonian operator H^ of the system. Therefore, the symmetry of the quantum mechanical system is expressed as Invariance of the Hamiltonian operator H^."

"Using S to represent a certain space-time transformation, that is, φ(S)=S^φ, the condition of unitarity is S^+S^=1, S^+=S^-1. Under space-time transformation, S remains unchanged The condition is that [H, S]=0, that is, there must be a conserved quantity related to the change S..."

While drawing a few strokes on the textbook with a pen, I quietly grasped this surprising inspiration.

Chen Zhou also suppressed the impulse in his heart, and continued to explain the content of conserved quantities and invariance.

He tries to get more out of it...

"After talking about the symmetric transformation, I'll tell you about space reflectivity and parity conservation..."

"Under the action of spatial reflection transformation I^, there is φ(x, y, z)→I^φ→φ(-x, -y, -z), obviously, I^ is a linear operator, and it is both The meter operator is also a unitary operator, that is, I^+=I^..."

"If the system is space-inversion symmetric, then [H, I]=0 is required, because I^ itself is an operator of a conserved quantity, and the eigenvalue I of I^ is +1 or -1, when it is When it is +1, it is an even par state, and -1 is an odd par state. Parity conservation requires that the parity of the state wave function does not change with time..."

The depth of Chen Zhou's explanation is getting deeper and deeper.

The students in the audience frowned more and more.

Even so, the pens in their hands never stopped for a moment.

They try their best to ensure that they can have a complete note afterwards for reviewing the content they don't understand.

Including the group of students surrounding the classroom, they also quickly recorded in their notebooks.

Among them, there are students who are about to graduate in their senior year, and there are also graduate students from the Department of Physics.

The content explained by Chen Zhou also began to gradually advance to the symmetry of identical particles.

In quantum mechanics, particles belonging to the same class are called identical particles.

This is also a unique property of quantum mechanics.

If there is no quantization of the state, there can be no identity.

The mutual symmetry of identical particles is also an indispensable part of the gauge field theory studied by Chen Zhou.

……

Time flies, and the time for this quantum mechanics class is almost over.

Chen Zhou also started the end of this class in good time.

Although compared with the number theory class in the morning, the quantum mechanics class in the afternoon did not advance the teaching materials too much.

There are only three chapters.

But the content in it is too rich and too much for any student.

So much so that after class, they were still staring at their own notes in a daze.

And those students gathered outside the classroom also looked at the blackboard, the content left by Chen Zhou in class, unwilling to leave for a long time.

Only in this class, Chen Zhou left behind the content on the blackboard.

With the inspiration of the exciting surprise that only he knew, he left quickly.

After leaving, Chen Zhou went straight to the dormitory.

I don't even plan to eat dinner.

In fact, when Chen Zhou was in class, he wanted to follow this surprise inspiration many times to carry out research on gauge theory.

But he still resisted the urge, trying to grasp more things in the process of teaching students.

Until the end of get out of class, he couldn't bear it anymore.

Chen Zhou, who returned to the dormitory, immediately got into his room.

After sitting down at the desk, Chen Zhou took out a fresh stack of A4 draft paper.

Then he opened the textbook he brought back and turned to the place where he had drawn with a pen.

Just glanced at it, the inspiration that surprised Chen Zhou.

It popped into my mind again...

(End of this chapter)