- #1
Physicsiscool
- 10
- 0
What concepts lead to the quantination of radii in the hydrogen atom, for example: r = r(o) * n squared?
Quantizing Radii in Hydrogen Atom: Concepts & Examples
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Discussion Overview
The discussion revolves around the concepts leading to the quantization of radii in the hydrogen atom, specifically the relationship expressed as r = r(o) * n squared. Participants explore theoretical foundations, assumptions, and implications of quantum mechanics in this context.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- Some participants discuss the role of energy and angular momentum operators having discrete spectra in the quantization of the hydrogen atom's radius.
- There is mention of the classical correspondence limit and canonical quantum mechanical relations as foundational to understanding why operators are quantized.
- One participant proposes that quantization arises from the electrical attraction between the electron and proton, alongside the condition that the path length must be a multiple of the de Broglie wavelength.
- Another participant challenges the simplification of de Broglie waves fitting into trajectories, suggesting that such descriptions are overly simplistic and not reflective of deeper quantum mechanical principles.
- A later reply expresses appreciation for the discussion, indicating that the information shared has been helpful.
Areas of Agreement / Disagreement
Participants express differing views on the adequacy of high-school level explanations of quantization, with some advocating for deeper understanding while others provide foundational concepts. The discussion remains unresolved regarding the best approach to conceptualizing quantization in quantum mechanics.
Contextual Notes
Limitations include varying assumptions about the applicability of classical mechanics to quantum systems, the dependence on specific definitions of operators, and the unresolved nature of the deeper implications of quantization.
- #2
masudr
- 931
- 0
The energy and angular momentum operators have discrete spectra when applied to the system of a hydrogen atom. And angular momentum being momentum * radius means that the radius is quantised.
To understand why the operators are quantised, you have to go all the way back to how we choose quantum operators, and that's down to satisfying the classical correspondence limit (in the limit as masses and momentums become large, results predicted by QM tends to results predicted by classical mechanics) as well as satisfying the canonical quantum mechanical relations (pq - qp = -ih etc).
To understand what these operators work on, you should be familiar with the Hilbert space. You should also understand Schrödinger's equation - that's what we use to derive radii levels.
To understand why the operators are quantised, you have to go all the way back to how we choose quantum operators, and that's down to satisfying the classical correspondence limit (in the limit as masses and momentums become large, results predicted by QM tends to results predicted by classical mechanics) as well as satisfying the canonical quantum mechanical relations (pq - qp = -ih etc).
To understand what these operators work on, you should be familiar with the Hilbert space. You should also understand Schrödinger's equation - that's what we use to derive radii levels.
- #3
Leo32
- 31
- 1
I read a text which showed this quantisation to come foreward from 2 assumptions:
- the electrical attraction between electron/proton keeping the electron in a circular path around the proton
- the fact that the length of the path needs to be a multiple of the brogly wavelength
It's too early in the morning at work to dash out the formula's from my head, but it should give you an idea.
Greetz,
Leo
- the electrical attraction between electron/proton keeping the electron in a circular path around the proton
- the fact that the length of the path needs to be a multiple of the brogly wavelength
It's too early in the morning at work to dash out the formula's from my head, but it should give you an idea.
Greetz,
Leo
- #4
dextercioby
Science Advisor
- 13,410
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The ideas of quantization are much more deeper than to picture all sorts of de Broglie waves and how they fit into trajectories,concepts which have nothing to do with the QM.This description is basically taught at high-school level and it's for the mass,not for the ones who are interested in going under he surface.I remember my 12-th grade manual,it was so stupid,when talking Bohr Hydrogen atom,it mentioned de Broglie's quantizing condition...I threw it away.Thankfully me and the teacher were lot smarter than the authors... 
- #5
Physicsiscool
- 10
- 0
This has been very helpful. Thank you!
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