Electron Probability of being at an location

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    Electron Probability
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SUMMARY

The discussion focuses on calculating the probability of an electron's location using quantum mechanics, specifically through Schrödinger's equation. To determine the probability density per unit volume (P/Δx^3), one must first define the potential function and the energy of the electron. After solving the Schrödinger equation to find the wave function, the position operator is applied to obtain the expected value for the electron's position. The conversation highlights the importance of understanding wave functions and quantum observables in this context.

PREREQUISITES
  • Understanding of Schrödinger's equation in quantum mechanics
  • Familiarity with wave functions and their properties
  • Knowledge of quantum observables and operators
  • Basic concepts of potential energy functions in quantum systems
NEXT STEPS
  • Study the solutions to the Schrödinger equation for various potential functions
  • Learn about quantum tunneling and its implications in particle physics
  • Explore the concept of probability density in quantum mechanics
  • Investigate the application of position operators on wave functions
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Students and professionals in physics, particularly those focusing on quantum mechanics, as well as researchers interested in electron behavior and probability calculations in quantum systems.

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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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 (Schrödinger's equation) and look for solutions to that equation. But then, once you find the wave equation (the solution to the Schrödinger 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
 
Sorry, TWest123 is a banned crackpot.
 

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