Lowest energy state with infinite and finite potential

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SUMMARY

The discussion centers on the energy states of an electron confined within a potential well, specifically comparing an infinite potential well (0 ≤ x ≤ L) with a ground state energy of 0.38 eV to a finite potential region (x > L) with a potential of 5 eV and a lowest eigenstate energy of 0.32 eV. The difference in energy levels is attributed to quantum tunneling, which allows the wavefunction to extend into the potential barrier, resulting in a lower energy state in the finite potential scenario. This phenomenon illustrates the impact of potential barriers on quantum mechanical systems.

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omiros
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Hello everyone and thanks for reading my post.

I have a problem with an electron, which actually is confined into a region 0 ≤ x≤ L with infinite potential around it, and its energy in the ground state is 0.38eV. Then on the x > L region the potential is 5eV and the energy of the lowest eigenstate is 0.32eV. What causes that difference?

Thanks for your time.
 
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The different potential causes a difference.

In the second case, the wavefunction will extend a bit into the x>L-region. This is similar to a larger potential well, so the ground state has a lower energy.
 
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I think the difference happen as a result of the TUNNELLING of the electron into the potential barrier.
 

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