Quantum Numbers: Why (3,-2,0,1/2) is Invalid

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Discussion Overview

The discussion centers around the validity of the quantum number set (3, -2, 0, 1/2) in the context of quantum mechanics. Participants explore the constraints on quantum numbers, particularly focusing on the principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (ml), and spin quantum number (ms).

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant states that for n=3, l=-2 is considered valid, but questions arise regarding the implications of this claim.
  • Another participant asserts that l must always be non-negative, thus invalidating l=-2.
  • A later reply clarifies that while l cannot be negative, ml can take on negative values.
  • Participants discuss the ranges of valid quantum numbers, noting that ml must satisfy the condition -l ≤ ml ≤ l.

Areas of Agreement / Disagreement

There is a general agreement that l cannot be negative, but the discussion reveals some confusion regarding the implications of this on the validity of the quantum number set. Multiple viewpoints exist on the interpretation of the quantum number constraints.

Contextual Notes

Participants express uncertainty about the implications of the quantum number rules and the specific ranges for ml and l. The discussion does not resolve the initial question regarding the validity of the quantum number set.

Feodalherren
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Homework Statement


Why isn't (3, -2 , 0 , 1/2) a valid quantum number?


Homework Equations





The Attempt at a Solution


n=3

so l = -2 is valid.

-l≤Ml≤l

2≤Ml≤-2
nonsensical statement. I don't know what to do...
 
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Feodalherren said:

Homework Statement


Why isn't (3, -2 , 0 , 1/2) a valid quantum number?

Homework Equations


The Attempt at a Solution


n=3

so l = -2 is valid.

-l≤Ml≤l

2≤Ml≤-2
nonsensical statement. I don't know what to do...

No, l=-2 is not valid. l is always non-negative.
 
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Ah so it's that simple... Thanks.
 
I agree.
n = 3
l = 0, 1, 2
ml = -2, -1, 0, 1, 2
ms = -1/2 or 1/2

l cannot be negative, but ml can be.
 

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