Uncertainty Principle: Position Uncertainty of Electrons

In summary, the conversation discusses the application of the uncertainty principle in the context of estimating the position of an electron in a sphere. The speaker questions the use of the radius instead of the diameter for uncertainty calculations, but it is noted that it does not affect the overall calculation. The conversation suggests looking for a derivation of the Heisenberg uncertainty principle from the commutator between x and p, which can be found in many sources such as a Quantum mechanics textbook or through a simple Google search.
  • #1
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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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  • #2
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.
 
  • #3
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.
 

FAQ: Uncertainty Principle: Position Uncertainty of Electrons

What is the Uncertainty Principle?

The Uncertainty Principle is a fundamental concept in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle. This means that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

What is the Position Uncertainty of Electrons?

The Position Uncertainty of Electrons refers to the fact that we cannot know the exact position of an electron at any given time. This is due to the wave-like nature of electrons, which means they do not have a definite position but rather exist as a probability distribution within an atom.

How does the Uncertainty Principle affect our understanding of the physical world?

The Uncertainty Principle challenges our classical understanding of the physical world, where we expect to be able to know the exact position and momentum of a particle at any given time. It suggests that at the quantum level, there are inherent limitations to our ability to measure and predict the behavior of particles.

What are the implications of the Uncertainty Principle in technology and everyday life?

The Uncertainty Principle has implications in various fields such as technology, where it plays a crucial role in the development of technologies such as computer chips and lasers. In everyday life, it helps us understand the behavior of atoms and molecules, which are the building blocks of all matter.

Can the Uncertainty Principle be violated or overcome?

No, the Uncertainty Principle is a fundamental principle of quantum mechanics and cannot be violated or overcome. It is a fundamental limit to our ability to measure and understand the behavior of particles at the quantum level.

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