Quantum Mechanics
It wasn't unusual for him to find her standing in the hallway of their institute, staring out of the windows and at the stars. It was actually closer to dawn than to the previous day's afternoon, but seeing her there didn't surprise him anymore. She often did that after long hours of research work in order to clear her mind and relax herself. He knew she was well aware of his presence despite the shadows hiding him."Sometimes, if you know the origin of a problem, it's easy to find a solution for it," she told him. She then redirected her attention from the sky to him and smiled sweetly. The dark circles under her eyes were a dead give away of how exhausted the exceptionally long day had left her. He imagined her computer in their laboratory, still turned on, running the calculations she had programmed it to run.
He walked over to her side. "But in the end, you still have to reexamine your solution and think if it is suitable for the situation that started the problem." He wondered if she was just talking about her research. It was rare that her words weren't pregnant with thoughts far beyond the science that they so often contemplated on.
She laughed shortly. "Yes, you're right," she replied. She looked him straight in the eye, "Why are you still up?" she asked.
"I woke up at around midnight. Can't sleep yet," he answered. He tried to read the expression on her face, but it was perfectly masked even as she searched his gaze. "What about you?"
"Oh, just thinking," she tilted her head and rested her cheek on her hand. "I'll be heading off to bed in a while, I imagine."
"Sometimes, the more you think about something, the more complicated it becomes," he reasoned out.
She laughed. "I'm well aware of that. But sometimes things get clearer..." there was a hitch in her voice and she glanced at the ground and he noticed that she did this to hide what little emotion she was unable to contain. "...as they did tonight."
He watched her curiously as she returned to what seemed to be counting the stars. There was a dullness to her eyes that told him she wasn't just physically tired.
"Problems that involve feelings are a lot like Quantum Mechanics," she told him, her voice breaking into his thoughts. There was an unreadable smile on her face that made him wonder if she was joking or not. "It's either there are no exact solutions for them or there is not enough information about them."
She was speaking in terms that were familiar to both of them. Physics. This way, she didn't have to give anything too explicit away if she wasn't joking, and it would be an interesting discussion if that was all she was after. He decided to work with the latter of his reasoning. "Like I said, you have to look at the appropriateness of the solution to the problem. Is the wave function well behaved and normalized?"
"I suppose I could use the perturbation theory, but the resulting differential equation is stiff to solve," she was pensive. They could pretend that nothing was wrong and try to resolve the problem while they lived their lives normally. "The function is rather well-behaved, but very sensitive to initial conditions." But, as with all volatile situations, even if their relationships weren't erratic and progressed steadily, the direction the relationship was headed relied heavily on where the situation started.
He found himself amused by the discussion. "You see, if the perturbing potential is large compared to the unperturbed Hamiltonian, the perturbation theory won't work." At the same time, he found that he was beginning to understand what she was talking about. If the problem was too large, there was no way that their lives could be lived as if there were no problems. That solution wouldn't work. "You should try WKB or the variation principle."
"I suppose you're right," she said. "If one method doesn't work, it would be wise to try another. But, at the same time, we still have to accept that we're working with approximations."
"Problems in Quantum Mechanics are a lot like problems that involve feelings," he finally stated. "Sometimes, there are no exact solutions. Approximating a solution is the last option and all we can do is make sure that we minimize the error."
She laughed softly, having her own analogy thrown back at her. She turned to him, the dullness still there, but the smile on her face touching her eyes almost imperceptibly. "That's true."
"It's getting late. The sun could rise on us," he pointed out the purplish sky.
"You're right," she wiped her glasses clean. "We should get some sleep."
"Yeah."
"Thanks."
"Goodnight."
posted by beautiful stranger @ 7:16 AM
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