Digimon Forum RolePlay - Waves vs Particles

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Topic: Waves vs Particles (Read 32 times)

haven
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Waves vs Particles
« Thread Started on Nov 7, 2009, 7:22pm »

"Since the invention of quantum mechanics, many people have struggled to resolve this dilemma. No one has yet succeeded," Milo's dad lectured, as Milo sat tapping his pencil against the desk in front of him. He knew this, they had already covered this, Milo didn't want a review... "It is as if the electrons start as particles at the electron gun, and finish as particles when they arrive at the detecotor, but the arrival pattern of electrons ovserved at the detecor is as if they travelled like waves in between."

For some reason, Milo kept thinking about the egg his sister found. The longer and longer he ignored it, the more his mind refused to let him. Why was Milo so anxious today? He felt as if there was something he needed to do today, some task hidden in the back of his memories, awaiting his attention. He attempted to pay attention to his dad, his professor, but he wasn't having much luck. He knew this already...

"We have seen that the mathematics of the interference curve can be summarized in a very simple equation." His dad continued, at the request of other students.

P₁₂ = (a₁ + a₂)²

P₁ = a²₁

P₂ = a²₂

"And as before, P₁₂ is not equal to the sum of P₁ and P₂." Milo wanted the test in front of him now. He want to fill in the answers, talk to his dad, and go home. "We conclude that electrons show wave-like interference in their arrival pattern despite the fact that they arrive in lumps, just like bullets. It is in this sense that we can say that quantum objects sometimes behave like a wave and sometimes behave like a particle."

P₁₂ ≠ P₁ + P₂

« Last Edit: Nov 8, 2009, 4:13pm by haven »

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abaddon
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Re: Waves vs Particles
« Reply #1 on Nov 8, 2009, 4:05pm »

It was not long after ten and Lumina was already bored and ansy. She sat in a chair in the back to the far left drawing some pictures, looking at and poking her bag on the floor quite often; to make sure no one noticed if it moved on its own. Her father was in the front giving a review to his students, which Lumina was not one of. Her brother Milo was though, and their mother was out of town so Lulu had to go to the class...and today was a test day! If only her dad would stop talking so she could just go and play and watch the egg already. Oh, she had a plan and knew just what to say to dear ol' dad, all while Milo had to stay and take a test. Ha, she loved it. Of course she knew he'd be out way before all the other kids, but at least it wasn't her. Although, it wouldn't be too long before her next test though.

Lumina looked up to her father every now and then to see if there would be any inkling of him ending his talk in the next few seconds. She had gotten good at pointing those out, as she was almost sure Milo had as well. She looked to her brother next, then the clock, and around the room - slowly. Most kids looked the same way, as if they probably were only half listening, if that, and just waiting to take the test - maybe repeating things over in their heads to make sure they wouldn't forget, in this waiting.

Waiting, waiting, waiting, Lulu thought up a tune and hummed in her head. Her eyes rolled up to the ceiling a lot in thought and wonderment at the fairytales playing out in her mind. She thought of the egg quite a bit, naturally, that was next to her in her black messenger bag. A few times she would glance at the board, but she didn't really understand a lot of it...at all. The mechanics of the subject that is quantam interested Lumina, sure, she even had read a few articles and chapters in book on it even, but she didn't think she'd go on to take a class in it. Astronomy was more what she was all about, much more.

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haven
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Re: Waves vs Particles
« Reply #2 on Nov 8, 2009, 4:08pm »

"You have two hours," The professor said, finally taking a seat at his desk. He gained Milo's complete attention, at long last, and that meant this was soon to be over. The tests were passed along student to student. Milo took one of the stapled stacks of papers, and passed the rest down the line. "But don't begin just yet."

Milo sighed, and his dad may have noticed.

"Remember that the completed assignments from last night..." Milo cringed a bit, he wouldn't like what his dad was about to say. He hadn't completed the assignments, he had been busy with the experiment. The more Milo sat there, the more and more he questioned whether he should even tell his father about the experiment. Milo wasn't exactly supposed to use his father's lab, or equipment, especially un-supervised. Milo was just... bored and curious. "Are worth twenty percent of your test grade. This test grade is fifty percent of your grade for the quarter. So, turn those in with your complete exams."

"So," His dad continued, and Milo hung his head. By default he could get no better than a B grade. He would have to make up for it, at some point, but Milo felt no need to be concerned. His grades would be fine, it's not as if a B was horrid. His father might feel differently, though. "I'll be at my desk for the duration of the test if you have any questions. You may begin."

Time to knock this test out.

« Last Edit: Nov 8, 2009, 4:13pm by haven »

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abaddon
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Re: Waves vs Particles
« Reply #3 on Nov 8, 2009, 4:23pm »

Finally, Lulu thought as soon as her dad took his seat. She was about to stand up for she thought the test would start right away, but he wasn't quite done. Lumina just strapped her bag over her shoulder while she was sitting, and waited yet some more.

When he was done talking, Lulu looked at the clock - 10:14. She stood up and made her way over to her father's desk quietly. When she was across from it she whispered to him, "Can I go the playground and draw this scene I've picturing for forever now, please?" Lulu smiled, and so did her father. He looked at her and then at her bag. "I wasn't sure what paper or pencils would be best, so I brought a lot of supplies, and you know I don't have any homework," she added, opening her bag a little. It was unusual of Lulu to bring a big bag of things so she felt the need to explain herself. Usually she brought a book, or multiple books, sometimes homework. Not that these visits happened often but anyway, she'd gotten into drawing lately so she had a cover. There was indeed pads of paper and pencils, erasers and sharpeners...on the top anyway. Underneath was the egg.

Lulu swayed a little bit, seeming anxious, hoping she hadn't seemed to suspicious. Really though, how was that suspicous at all? It wasn't, so calm down, Lulu! She told herself, smiling a little. Her dad just nodded his head and laughed a little. She glided off and out the door, down the hill "and through the woods to grandmother's house we go," she sang. No, she wasn't going to grandma's house, she was headed towards the playground but not to draw either.

With a skip and a hop, after walking quite a ways, she was there. It was quite a nice day and she was definitely thankful for that. The sun was bright and she was warm, a little too warm. "Phew," she said as she sat down and rolled up her sleeves. She carefully set the bag down next to her and just took a breather.

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Re: Waves vs Particles
« Reply #4 on Nov 9, 2009, 3:06pm »

(1) In the equation Δx Δp = ћ, what do the symbols Δx and Δp mean?

Milo felt like he wasn't concentrating. He had to be, at least a bit, because he was writing his answers quickly. He didn't need time to think about the questions, but his mind kept thinking even as he was writing. Not about the exam though, but his mind was elsewhere. Back to the egg her sister found, and now proceeded to exit the classroom with. Did she plan on doing something with it? Milo would have to hunt her down after he was done, which hopefully wouldn't be too long...

(13) For a particle in a box, (a) is 3.5 wavelengths between the walls a possibility? (b) 5.0 wavelengths? (c) 1.75 wavelengths? Keep in mind that the wave in the box must interfere constructively with itself after one round trip between the walls.

Knock on wood. It seems solid. It is solid. But probe more deeply and you encounter other worlds.THis includes the discovery that matter has wave properties, the realization that the fundamental laws of nature are laws of probability, not laws of certainty; the understanding that there is a limit in principle to the acacuracy with which certain propertie of matter can be measured; the discovery that electrons spin about an axis that can point in onl two posible direction; the predictoion that single electron or photons can be moving in two or more different ways simultaneously. Milo couldn't picture these concepts, in any real sense, but he could understand. He could do the math.

(24) In the de Broglie equation λ = [i]h/p, Planck's constant is h[/h] = 6.6 x 10³⁴ kg m²/s and the momentum [i]p is equal to mv, the product of mass and velocity. (a) Calculate the wavelength of an electron of mass 9.1 x10³¹ kg moving at 2 x 10⁶ m/s.[/i]

Almost done... Milo continued to scribe his answers down on paper. He kept visualizing himself completing the test, handing it in to his father. What would he say when he found out Milo hadn't done his homework? His father couldn't make an exception for him, he could only get a B on the exam. His father couldn't be that angry, Milo was his best student. Still somehow... Milo felt like he shouldn't tell him.

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