Uncertainty Principle: Position Uncertainty of Electrons

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SUMMARY

The discussion centers on the application of the uncertainty principle in quantum mechanics, specifically regarding the position uncertainty of electrons. Participants highlight that using the radius of a sphere (delta 'r') instead of the diameter does not affect calculations but raises conceptual questions. The Heisenberg uncertainty principle is emphasized, with a recommendation to derive it from the commutator between position (x) and momentum (p). Key resources mentioned include Sakurai's "Modern Quantum Mechanics" for further understanding.

PREREQUISITES
  • Understanding of the Heisenberg uncertainty principle
  • Familiarity with quantum mechanics concepts
  • Knowledge of commutators in quantum physics
  • Basic grasp of electron behavior in quantum systems
NEXT STEPS
  • Study the derivation of the Heisenberg uncertainty principle from the commutator between position and momentum
  • Read Sakurai's "Modern Quantum Mechanics" for comprehensive insights
  • Explore the implications of position uncertainty in quantum mechanics
  • Investigate the mathematical formulation of uncertainty in quantum systems
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Students of quantum mechanics, physicists, and anyone interested in the foundational principles of quantum theory and electron behavior.

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In application of uncertainity principle i read,if we suppose electron in a sphere of radius r then we assume unertainity of position as delta 'r',instead of taking diameter as uncertainity.Though it will not effect the calculations at all,but conceptually and physically what could be the reason behind it.I was unable to come to any result.
 
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I don't see the point of that sort of calculations, but once you've decided to do a calculation like that, it doesn't matter if you use the radius or the diameter since you're only trying to estimate an order of magnitude.
 
You might want to look for a derivation of the Heisenberg uncertainty principle from the commutator between x and p, it is quite trivial. You will find many pages if you google.

You can also look it up in almost any Quantum mechanics textbook, Sakurai - Modern Quantum mechanics, for instance.
 

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