Infinitely large quantum number

In summary, the calculation of root mean square fluctuation in position for an electron confined in a box and in a state with a large quantum number n involves using a function that is a solution of Schrodinger's equation with the appropriate potential, which in this case is an infinite square well. This can be found in common textbook exercises or by searching for "infinite square well quantum" online.
  • #1
terp.asessed
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Hi--could someone explain how can one calculate for the root mean square fluctation in position when an electron (confined in a box) is quantum-mechanical and happens to be in a state (an infinitely large quantum number n) and why?
I do know how to calculate root mean square fluctation in position with the given function and n, as in (root-mean)2 = <x2> - <x>2 but am not sure how to do this with huge n value. Do I just use Schrodinger equation, where V (potential) is equal to 0?
 
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  • #2
You don't use Schrodinger's equation, you use a function that is a solution of Schrodinger's equation with the appropriate potential (which in this case is an infinite square well the width of the box). This is a common textbook exercise so googling for "infinite square well quantum" or the like will find you some worked examples.
 

Related to Infinitely large quantum number

What is an infinitely large quantum number?

An infinitely large quantum number is a theoretical concept in quantum mechanics that represents the highest possible energy level of an electron in an atom. It is often used to simplify calculations and understand the behavior of electrons in highly excited states.

How does an infinitely large quantum number affect an atom?

An infinitely large quantum number can significantly alter the behavior of an atom. It can cause the electron to be highly unstable and easily ionized, leading to the breakdown of the atom's structure and properties.

Can an infinitely large quantum number exist in reality?

No, an infinitely large quantum number is a theoretical concept and does not exist in reality. It is used as a tool to understand the behavior of electrons in highly excited states but does not have a physical manifestation.

What is the relationship between an infinitely large quantum number and the energy level of an electron?

The energy level of an electron increases as the quantum number increases. As the quantum number approaches infinity, the energy level also approaches infinity, making the electron highly unstable and easily ionized.

How does an infinitely large quantum number affect the size of an atom?

An infinitely large quantum number can cause the size of an atom to increase significantly. This is due to the electron being highly excited and occupying a larger orbit, leading to an increase in the size of the atom's outermost electron shell.

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