Why Are There Blank Spaces in Quantum Mechanics Orbitals?

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Discussion Overview

The discussion revolves around the question of why there are blank spaces in quantum mechanics orbitals, particularly focusing on the interpretation of orbital shapes and the underlying mathematics of quantum mechanics. The scope includes conceptual understanding and mathematical reasoning related to the Schrödinger equation.

Discussion Character

  • Exploratory, Conceptual clarification, Technical explanation

Main Points Raised

  • One participant expresses curiosity about the lack of explanation in their chemistry book regarding the blank spaces in orbitals and seeks insights from others.
  • Another participant suggests that a simple answer is unlikely and that understanding the phenomenon requires advanced mathematics related to the Schrödinger equation.
  • A different participant explains that the blank spaces result from solving the Schrödinger equation for electrons influenced by the Coulomb force, specifically referencing the hydrogen atom as a case study.
  • One participant indicates a reluctance to engage with the necessary mathematics at the moment due to other academic commitments.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a definitive explanation for the blank spaces in orbitals. There are multiple viewpoints regarding the complexity of the mathematics involved and the nature of the inquiry itself.

Contextual Notes

The discussion highlights the dependence on advanced mathematical concepts and the limitations of introductory materials in addressing deeper questions about quantum mechanics.

Danilo Boskovic
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So, I am kind of learning QM on my own, and through my chemistry book. It doesn't explain any further than the shapes of orbitals, and I am wondering did anyone found out why is space in the orbitals between the clusters of probability blank.
 
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I think there is no simple answer to that question which would not require advanced mathematics appearing when one explicitly solves the Schrödinger equation.
 
Danilo Boskovic said:
So, I'm kind of learning QM on my own, and through my chemistry book. It doesn't explain any further than the shapes of orbitals, and I am wondering did anyone found out why is space in the orbitals between the clusters of probability blank.

That's the result that you get when you solve Schrödinger's equation for electrons moving under the influence of the Coulomb force between them and the nucleus. If you google for "Schrödinger equation hydrogen atom" you'll find many derivations of this result for hydrogen, which is the simplest case - one electron whose mass is small compared with that of the nucleus. (You'll also find out why your chemistry book doesn't go into these details :smile:)

If you're asking if there's some deeper mechanism that says it has to come out this way, that's tantamount to asking why the universe works according to Schrödinger's equation, and science can't answer that question.
 
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not really into spending time in learning new math right now.. i got an university entrance examination to pass :D . Thanks anyways. I will look into it later when i have time.
 

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