Electron One Split Energy Probability Density Function

In summary, the conversation discusses finding the probability density function for an infinitesimal energy range by converting the coordinate space wave function to a momentum space wave function and integrating the absolute value of the squared momentum space wave function over the energy interval. It is noted that the normalization constant should be found by integrating the square of the magnitude of the wave function.
  • #1
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Homework Statement


https://www.physicsforums.com/attachment.php?attachmentid=69371&d=1399142463

2. The attempt at a solution
I am working on the last problem now.
Here is what I have got so far. Basically I have converted the coordinate space wave function to a momentum space wave function. Then one can associate an Energy interval to a momentum space interval and integrate the absolute value of momentum space wave function squared in that interval to find the probability density function as a function of Energy. But somehow I am getting a weird result.
View attachment Übung 19.pdf
 
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  • #2
When finding the normalization constant, c, make sure you integrate the square of the magnitude of the wave function.

You are asked to find the probability density for an infinitesimal range E to E + dE. So, you don't need to integrate over an interval.

Your Fourier transform to momentum space looks good to me.
 
  • #3
Thanks. Yeah you're right about the normalization constant, really sloppy on my side.
Thanks for your hint.
 

1. What is an Electron One Split Energy Probability Density Function?

An Electron One Split Energy Probability Density Function is a mathematical function that describes the probability of finding an electron in a specific energy state within an atom. It takes into account the splitting of energy levels due to various factors, such as spin and magnetic field.

2. How is an Electron One Split Energy Probability Density Function calculated?

The function is calculated using quantum mechanics, specifically the Schrödinger equation. It involves solving for the wave function of the electron and then using it to calculate the probability density at each point in space.

3. What does the Electron One Split Energy Probability Density Function tell us about electrons?

The function provides information about the distribution of electrons within an atom, including their energy levels and positions. It also gives insight into the behavior and properties of electrons, such as their spin and magnetic moments.

4. How does the Electron One Split Energy Probability Density Function relate to atomic orbitals?

Atomic orbitals are regions in space where the probability of finding an electron is high. The Electron One Split Energy Probability Density Function gives the exact shape and size of these orbitals, as well as the probability of finding an electron at any given point within the orbital.

5. Can the Electron One Split Energy Probability Density Function be visualized?

Yes, the function can be visualized using various tools and software, such as molecular modeling programs. This allows scientists to better understand the distribution of electrons within an atom and how it relates to the properties and behavior of matter at the atomic level.

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