Magnetic Quantum No: Angular Momentum, Electron Orbit Orientation

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Discussion Overview

The discussion revolves around the implications of the magnetic quantum number being zero on the angular momentum of electrons, particularly in relation to their orientation in a magnetic field. Participants explore the geometry of electron orbitals, specifically the s-orbital, and the characteristics of angular momentum vectors in the context of quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant states that if the magnetic quantum number is zero, the component of angular momentum along the magnetic field direction will also be zero, prompting questions about the electron orbit's orientation.
  • Another participant references the geometry of the s-orbital, suggesting it has relevance to the discussion of angular momentum.
  • A participant discusses the implications of having a zero z-component for any vector, questioning the possible directions of that vector and their common characteristics.
  • A later reply elaborates on the distinction between having a magnetic quantum number m = 0 deterministically leading to zero angular momentum and the possibility of m = 0 being a statistical implication of zero angular momentum in certain contexts, particularly in relation to the s-orbital.
  • The same participant concludes that a planar vector representation should not correspond to quantum states with m = 0, suggesting a nuanced view of the relationship between quantum states and angular momentum.

Areas of Agreement / Disagreement

Participants express differing views on the implications of a magnetic quantum number of zero and its relationship to angular momentum and orbital orientation. The discussion remains unresolved with multiple competing perspectives presented.

Contextual Notes

The discussion includes assumptions about the orientation of magnetic fields and the nature of quantum states, which may not be universally applicable. There are also unresolved mathematical implications regarding the relationship between quantum numbers and angular momentum.

Who May Find This Useful

This discussion may be of interest to those studying quantum mechanics, particularly in relation to angular momentum, magnetic quantum numbers, and the geometry of electron orbitals.

mkbh_10
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If magnetic quantum no. is zero then component of angular momentum along magnetic field direction will be zero , what does it mean ? What can be said about the orientation of the electron orbit in this case ?
 
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Look at the geometry of the s-orbital. What does it look like?

Zz.
 
Suppose the magnetic field is along the z-direction (which is what we usually assume). If the z-component of a vector (any vector, not just the angular momentum vector) is zero, what are the possible directions of that vector? What characteristic do all those directions have in common?
 
jtbell said:
Suppose the magnetic field is along the z-direction (which is what we usually assume). If the z-component of a vector (any vector, not just the angular momentum vector) is zero, what are the possible directions of that vector? What characteristic do all those directions have in common?

Ok, then we have the planar configuration for the referred vector. But one thing is m = 0 imply deterministically the Lz to be zero. Another thing is to have m = 0 as an implication of Lz to be ZERO in some statistical sense, i.e. in average. As in the first answer, the s orbital (spherical) has zero Lz, but just when done the average.

Thus, if a quantum state has an associated eigenvalue m = 0, we may conclude that Lz aplied on this state yield eigenvalue zero, which has to do with spatially global feature of the state.


In conclusion, I think that the picture of a planar vector must not correspond to quantum states with m = 0.

Best wishes

DaTario
 
Last edited:

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