Infinite Square Well with Multiple Particles

Thread starter sarahjohn
Start date Jul 7, 2021
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Infinite Infinite square well Multiple Particles Square Square well

AI Thread Summary

The discussion revolves around calculating energy levels in an infinite square well for a system with multiple particles, specifically seven electrons. The initial calculation using the formula En = (h2*n2) / (8*m*L2) yielded an incorrect energy value of E1 = 0.06017 eV. The error was identified as failing to account for the presence of seven electrons in the system. After acknowledging the mistake, the user successfully resolved the issue. This highlights the importance of considering particle interactions in quantum mechanics calculations.

Jul 7, 2021

sarahjohn

Homework Statement: An infinitely deep square well has width L = 2.5 nm. The potential energy is V = 0 eV inside the well (i.e., for 0 ≤ x ≤ L). Seven electrons are trapped in the well.

1)What is the ground state (lowest) energy of this seven electron system?
2)What is the energy of the first excited state of the system?
NOTE: The first excited state is the one that has the lowest energy that is larger than the ground state energy.
3)What is the energy of the second excited state of the system?

Relevant Equations: En = (h^2 * n^2) / (8 * m * L^2)

Using the equation En = (h²*n² ) / (8*m*L²), I got that E1 = 0.06017eV but the answer is not correct.

Last edited: Jul 7, 2021

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Jul 7, 2021

TSny

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Have you taken into account that you have seven electrons?

Jul 9, 2021

sarahjohn

TSny said:

Have you taken into account that you have seven electrons?

I realized that was my mistake and figured it out. Thank you!

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