The villainous young lady is actually a scientific research genius!

For the next period of time, Lu Zhaozhao received special permission from Principal Chen—she was exempt from attending first-year high school courses, but she had to get first place in every exam.

Lu Zhaozhao agreed.

She spent her days at Peking University and the Institute of Physics, and her evenings at her maternal grandfather's house reading and doing exercises.

This situation lasted for two weeks.

……

Monday morning, Physics Department, Beijing University.

Gu Chengyuan stood on the podium in the lecture hall, explaining the basic concepts of quantum mechanics.

There were more than seventy third-year students sitting in the audience. In the last row, in a corner, Lu Zhaozhao was writing something in her notebook.

"...The Schrödinger equation describes the evolution of the wave function of a quantum system over time."

Gu Chengyuan wrote the formula on the blackboard, "This equation is non-relativistic and only applies to..."

Lu Zhaozhao looked up: "Professor Gu, when the Schrödinger equation deals with multi-particle systems, the dimensionality of the Hilbert space increases explosively, and the computational complexity rises exponentially. Are there any more efficient approximation methods?"

The classroom fell silent.

Several students turned around and stared at Lu Zhaozhao as if she were a monster.

Gu Chengyuan adjusted his glasses, a hint of admiration flashing in his eyes:

"Are you referring to density functional theory?"

"right."

Lu Zhaozhao nodded, "Using electron density instead of the wave function as the basic variable simplifies the many-body problem into a single-body problem. Although the exact form of the commutative correlation functional is still unknown, the local density approximation is sufficient in many cases."

A collective gasp filled the classroom.

The boy sitting in the front row turned around and asked the student next to him in a low voice:

"Who's that kid in the school uniform? Can you even understand what they're saying?"

"It would be strange if I could understand it... It sounds like someone is Professor Gu's relative?"

"A relative? That's incredible..."

Gu Chengyuan quickly wrote several formulas on the blackboard.

"Zhao Zhao is right. Density functional theory is one of the most effective methods for dealing with multi-electron systems."

He turned to look at the audience, "However, this content belongs to graduate courses, so you don't need to master it now."

Lu Zhaozhao lowered her head and continued deriving formulas in her notebook.

After class, Gu Chengyuan walked to the last row.

"Zhaozhao, come to the office with me."

"Um."

The two walked out of the classroom, and behind them came the murmurs of the students.

"Who is that girl? She seems to know more than we do..."

"I heard she's Professor Gu's niece, a first-year high school student."

"First year of high school?! I've wasted the last three years of my education..."

In the office, Gu Chengyuan poured Lu Zhaozhao a glass of water.

"Zhaozhao, how much do you know about density functional theory?"

Lu Zhaozhao took the water glass.

"I understand the basic framework. The Hohenberg-Kohn theorem, the Kohn-Sham equation, and various approximate forms of commutative correlation functionals."

She paused for a moment, then added, "However, current computer performance is too poor, and many ideas cannot be verified."

Gu Chengyuan remained silent for a few seconds.

He knew that Zhao Zhao was no ordinary genius.

This child's understanding of physics has surpassed that of the vast majority of graduate students, and even many teachers.

"How is your grandfather doing?"

"good."

Lu Zhaozhao's tone remained calm. "Last week, I helped him derive a formula about neutron scattering cross section, which he said could be used in reactor design."

Gu Chengyuan tapped his fingers on the table.

"Zhaozhao, with your current level, you can completely skip high school and go straight to university."

"No rush."

Lu Zhaozhao shook her head, "During high school, you can participate in various competitions, and winning awards will help with future research funding applications. Besides..."

She raised her eyes, her dark eyes radiating confidence:

"I need more time to solidify my foundation."

Gu Chengyuan nodded.

He understood Zhao Zhao's thoughts.

This child isn't after empty fame; she genuinely wants to achieve results.

"Then you can continue to sit in on the classes during this period. If you need anything, just let me know."

"it is good."

……

Wednesday afternoon, Institute of Physics.

Gu Weimin stood in front of the experimental table, staring at the sample in the liquid nitrogen cooling device.

Lu Zhaozhao stood beside him, holding a notebook in her hand:

"Grandpa, the critical temperature of this yttrium barium copper oxide sample is 5 Kelvin lower than the theoretical prediction."

Gu Weimin frowned:

"The manufacturing process has been optimized, but it still doesn't meet expectations."

Lu Zhaozhao glanced at the temperature curve, then looked at the crystal structure data of the sample:

"The problem is not with the manufacturing process."

She pointed to the X-ray diffraction pattern.

"The interlayer spacing of the copper oxide layer is too large by about 0.02 angstroms, which will affect the electron pairing mechanism."

Gu Weimin paused for a moment and then re-examined the preparation records.

Sure enough, the oxygen partial pressure setting during the final annealing was incorrect.

He remade the sample according to Lu Zhaozhao's suggestion.

The critical temperature was raised to 93 Kelvin, which is in full line with theoretical expectations.

Gu Weimin turned around, looked at Lu Zhaozhao, his eyes full of satisfaction.

"Zhaozhao, your understanding of crystal structure and superconductivity mechanism..."

"Basic operations."

Lu Zhaozhao said calmly, "The key to high-temperature superconductivity lies in the electronic state density distribution of the copper-oxygen interface, and the interlayer spacing directly affects the formation of Cooper pairs."

Gu Weimin smiled and said nothing more.

"Grandpa, this set of data can be used to verify high-temperature superconductivity mechanisms that go beyond the framework of the BCS theory."

Lu Zhaozhao opened her notebook. "If the results meet expectations, we can compile them into a paper and submit it to Physical Review Letters. I'm considering using the theory of strongly correlated electron systems to explain the influence mechanism of antiferromagnetic fluctuations on superconducting pairing."

Gu Weimin nodded.

"You write the first draft, and I'll help you polish it. If we can make a breakthrough in this area, it will be of great significance for understanding the microscopic mechanisms of high-temperature superconductivity."

"it is good."

The two continued working, the only sounds in the lab being the hissing of boiling liquid nitrogen and the hum of the instruments.

……

Saturday morning, Beijing No. 1 High School competition training room.

Yan Zheng stood on the podium, holding a piece of chalk, and wrote a number theory problem on the blackboard.

"This question was the final question in last year's national competition, and the pass rate that year was less than 5%."

He turned to the audience and said, "You have thirty minutes. Raise your hand if you can do it."

The classroom was quiet.

The students were engrossed in calculations, their scratch paper filled with formulas.

Five minutes later, Lu Zhaozhao put down her pen and raised her hand.

Yan Zheng glanced at her.

"Lu Zhaozhao, come up and speak."

Lu Zhaozhao walked to the front of the classroom, picked up the chalk, and quickly wrote down the solution steps on the blackboard.

"The key to this problem is to construct an auxiliary function and then use Fermat's Little Theorem and Euler's Theorem..."

Her handwriting was neat, her logic was clear, and every step of her deduction was accurate.

A few minutes later, the complete solution appeared on the blackboard.

Yan Zheng stared at the blackboard for a few seconds and nodded.

"Sit down."

Lu Zhaozhao returned to her seat and continued reading.

Whispers could be heard coming from the classroom.

"How could she be so fast..."

"I didn't even understand the question..."

"Is this the power of a perfect scorer? He's going berserk..."

Lu An'an, sitting in the corner, gripped her pen tightly.

She stared at Lu Zhaozhao's back, a sinister glint in her eyes.

The pen in her hand deformed slightly under her force.

Lu Zhaozhao...

You wait...

……

Sunday afternoon, physics competition training room.

Zhou Mingyuan explained the complex issues of electromagnetic induction on the podium.

"...When a conductor moves in a non-uniform magnetic field, the calculation of the induced electromotive force requires..."

Lu Zhaozhao raised her head.

"Professor Zhou, if we consider relativistic effects, will the conclusion be different?"

Zhou Mingyuan was stunned for a moment.

"Relativistic effects?"

"right."

"Within the framework of relativity, electric and magnetic fields are different components of the same electromagnetic field tensor and can be transformed into each other by the Lorentz transformation."

Zhou Mingyuan remained silent for a few seconds.

He pushed up his glasses:

"You're right. But high school physics competitions don't cover relativity, so you don't need to worry about that now."

Lu Zhaozhao nodded and said nothing more.

Shen Yi watched Lu Zhaozhao's retreating figure, a flash of jealousy in his eyes.

"What are you pretending for..."

He muttered to himself, "It's just about knowing how to solve a few problems..."

……

Time flew by amidst the intense study and research, and before we knew it, it was time for the National High School Mathematics League.