Electron Probability of being at an location

In summary, the conversation discussed the possibility of using an equation to determine the probability of an electron's location using elementary constants and energy. The process involves defining the potential function and energy of the particle, setting up the differential equation, finding the wave equation, and applying the position operator to obtain the expected value for the particle's position. The conversation also mentioned examples of solving 1D particle wells.
  • #1
twest123
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Okay, Basically I was wondering is if there is a equation that can be used to tell what the probability of a electron being at that location is per unit of volume (P/Δx^3) from elementary constants and Energy only if possible also having never used the equation before I would like if you would explain how to use it.
 
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  • #2
Well, the first thing is that you need to define the "setting". That is, the shape of the potential function in which the particle is being measured, and also the energy of the particle itself. Then you can set up the differential equation (Schrodinger's equation) and look for solutions to that equation. But then, once you find the wave equation (the solution to the Schrodinger equation), your works still not done; you then have to apply the position operator to the wave function (in QM, observables are operations on the wave function) and that will give you your "expected value" for the position of the particle.

I've only solved 1D particle wells, myself. But it's enough to see things like tunneling and get a feel for the different outcomes.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/pbox.html
 
  • #3
Sorry, TWest123 is a banned crackpot.
 

FAQ: Electron Probability of being at an location

What is electron probability of being at a specific location?

The electron probability of being at a specific location refers to the likelihood of finding an electron at a particular point in space. This probability is represented by a wave function, which describes the behavior of electrons in the quantum mechanical model of the atom.

How is electron probability calculated?

Electron probability is calculated using the Schrödinger equation, which takes into account the energy of the electron and the forces acting on it. The result is a wave function that can be used to determine the probability of finding the electron at any given point in space.

What factors affect electron probability?

The electron probability at a given location is affected by several factors. These include the energy level of the electron, the presence of other particles or forces in the vicinity, and the shape and size of the orbital in which the electron is located.

How does electron probability relate to electron density?

Electron probability and electron density are closely related concepts. Electron density refers to the concentration of electrons in a given region of space, while electron probability describes the likelihood of finding an electron in that region. Higher electron probability corresponds to higher electron density.

Can electron probability be visualized?

While electron probability cannot be directly observed, it can be visualized using tools such as quantum mechanical models and probability maps. These visualizations can give us a better understanding of the behavior of electrons in atoms and molecules.

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