Energy levels in a potential well

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SUMMARY

The ground state energy in a potential well is not zero due to the principles of quantum mechanics, specifically the definition of energy states governed by the principal quantum number (n). The energy formula is given by En = -me4 / (2h2n2), where n starts at 1, not 0, to prevent infinite energy, which corresponds to an electron being separated from the atom. The presence of Coulomb potential ensures that energy levels are always negative, indicating that energy is never zero in an atom.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the concept of quantum numbers
  • Knowledge of Coulomb potential in atomic physics
  • Basic grasp of energy state equations
NEXT STEPS
  • Study the derivation of the energy levels in quantum mechanics
  • Explore the implications of the Coulomb potential on atomic structure
  • Learn about the significance of quantum numbers in determining electron configurations
  • Investigate the concept of zero-point energy in quantum systems
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Students and professionals in physics, particularly those focusing on quantum mechanics, atomic physics, and anyone seeking to understand energy levels in potential wells.

physmile
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I know this question seems very simple which is why its bugging me so much:
Why is the ground state energy not zero?
A simple answer would be greatly appreciated
 
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physmile said:
I know this question seems very simple which is why its bugging me so much:
Why is the ground state energy not zero?
A simple answer would be greatly appreciated

Energy states are defined with principle quantum number (n). n= 1,2,3...

E_{n}= \frac{-me^{4}}{2h^{2}n^{2}}

"Ground state" means 1st term in serie of "n" and it's 1.

You may ask, why doesn't "n" start from zero? When you put 0 for n, energy goes to infinite and that mean electron separated from atom. That's why n doesn't start from zero.


And finally your question, there is allways a energy in an atom because of the Coloumb potential. The energy never been zero.
 
Only changes in energy are physical. You can define the ground state of any particular system to have zero energy.
 
Thank you very much for your help torehan!
 

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