Loyce didn’t even pick up a pen. She simply tilted her head, as if recalling a common fact, and her clear voice flowed smoothly through the microphone.
“The wave function, ψ(x,t), is a complex function describing the state of a microscopic particle. According to Born's statistical interpretation, |ψ(x,t)|²dx represents the probability of finding the particle within the interval dx around position x at time t. Therefore, the position probability density is ρ(x,t) = |ψ(x,t)|².”
Her delivery was unhurried, each word precise and hitting the core of the concept.
Hallie’s face grew even darker. She hadn’t expected such a fluent and profound answer. This wasn't going well.
Refusing to be beaten, she immediately threw out a second question, leaping several levels in difficulty. “Second question! Theoretical mechanics! Briefly describe D'Alembert's principle and express it in the form of the principle of virtual work! Explain its significance in analytical mechanics!”
Still poised, Loyce answered after a brief moment of thought. “D'Alembert's principle states that for a system of mass points subject to constraints, at any given instant…”
As Loyce continued her explanation, the students in the audience felt like they were listening to a foreign language. They recognized the individual words, but strung together, they formed incomprehensible symbols and meanings.
The only ones who understood were the physics and math teachers. At that moment, they were frozen like statues, their faces etched with utter shock and disbelief.
These questions were far beyond the scope of a high school curriculum! Hallie was testing graduate-level knowledge.
They stared at Loyce as if she were a goddess of mathematics who had walked straight out of a textbook. Not only did she answer perfectly, but she also provided textbook-level structural insights and profound physical interpretations.
This wasn't some “worthless tutor.” This was the kind of deep understanding you’d expect from a top-tier university professor.
After finishing her explanation, Loyce added, “Since you brought up this principle and its relation to quantum mechanics, I’d like to ask you, Hallie, how one might accurately measure the interaction between entangled quantum states.”
Loyce's response included an extension and a counter-question. When she unexpectedly turned the tables on Hallie with a more difficult problem, Hallie completely froze.
Her own doctoral studies hadn't been in pure physics. She had only happened to read a paper on Hallie's earlier question—an obscure article in Arabic that she had barely managed to comprehend with a translation tool. She never imagined Loyce would actually be able to answer it, let alone this.

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