Understanding Standing Waves in Hydrogen with Animation and Quantum Mechanics

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Discussion Overview

The discussion revolves around the representation of standing waves in hydrogen, particularly in relation to quantum mechanics and visualizations of atomic structures. Participants explore the validity of an animation as a representation of these concepts and inquire about techniques used to visualize hydrogen atoms.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant questions whether a specific animation can represent a standing wave in hydrogen and suggests that if it rotated, it could represent the probability cloud in quantum mechanics.
  • Another participant argues that the animation is not relevant to quantum mechanics, emphasizing that particles in quantum mechanics do not behave like moving dots as depicted in the animation.
  • A participant explains that the Schrödinger equation for an electron in a central potential is used to describe the probability amplitude of an electron around the nucleus, which can be visualized by coloring regions based on probability amplitude squared.
  • There is a request for information on whether modern technology can provide images of hydrogen atoms, indicating interest in practical applications of quantum mechanics.
  • A participant shares a link to an article about the first image of a hydrogen atom's orbital structure, contributing to the discussion on visualization techniques.
  • Another participant expresses gratitude for the information provided and asks for comments on the ground state of hydrogen.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of the animation to quantum mechanics, with some asserting it is not appropriate while others explore its potential implications. The discussion on visualization techniques and the Schrödinger equation appears to be more aligned, but no consensus is reached on the broader topic of representing standing waves in hydrogen.

Contextual Notes

Participants mention the complexity of solving the Schrödinger equation for the hydrogen atom, indicating that a solid understanding of mathematics is necessary to grasp the solutions fully. There are also references to the limitations of current visualization techniques and the nature of quantum particles.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of quantum mechanics, particularly those interested in atomic structure visualization and the mathematical foundations of quantum theory.

bobie
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Can this animation http://en.wikipedia.org/wiki/File:GravitationalWave_PlusPolarization.gif be a good representation of a standing wave in Hydrogen?
If the wave rotated on the normal direction could then be a representation of the probability cloud in QM?
Can you give me a link whre to learn how, with which technique they get a picture of an atom of H?
 
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bobie said:
Can this animation http://en.wikipedia.org/wiki/File:GravitationalWave_PlusPolarization.gif be a good representation of a standing wave in Hydrogen?
No, it's a picture of something completely different. One very big hint that it has nothing to do with quantum mechanics is that each little moving dot in the picture represents a particle - and if you've heard it once you've heard it 83 bazillion times here - in quantum mechanics particles are not like little dots that have a position and move around.

Can you give me a link where to learn how, with which technique they get a picture of an atom of H?

The technique we use is to write down the Schrödinger equation for an electron in a central potential, and solve it. The solution is a function that describes the probability amplitude for the electron being localized within a particular region around the nucleus. Given this, we can draw a picture just by coloring all the points where the probability amplitude squared is greater than some value - that will give us the shape of the region within the electron will be found with a given probability.

Googling for "hydrogen atom solution Schrödinger equation" finds many hits, although as the first one from hyperphysics says, "The solution of the Schrödinger equation for the hydrogen atom is a formidable mathematical problem...", which is a polite way of saying that there's no substitute for actually learning enough math to follow the solution. It's within the reach of any second-year class of differential equations.
 
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Nugatory said:
The technique we use is to write down the Schrödinger equation.

Thanks, Nugatory, I was wondering if it is possible with modern technology (and microscopes) to scan and get sort of a picture of an atom of hydrogen.
 
Thanks a lot, Bill, that is what I was looking for. Can you comment on the ground state?
 

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