"The energy levels of a particle in a 3D box with sides of length a are:(adsbygoogle = window.adsbygoogle || []).push({});

E = (n_x^2 + n_y^2 + n_z^2)[(h-bar)^2.(pi)^2]/2ma^2

where n_x, n_y and n_z are integers and greater than zero.

If 10 electrons are placed in such a box, what is the lowest possible value for the summed energy of the electrons? Show your working".

I know that the electrons must have different values of n_x, n_y, n_z, but I don't know where to start, besides that. Which values of n_x, n_y and n_z am I meant to use and how do I vary them for different levels? If it was a one dimensional thing, I'd just use n = 1, 2, 3, .., right? For a 3D case, I'm not sure how to deal with having 3 n terms there. Do I need to do stuff with the quantum numbers l and m_l too?

Any help appreciated, thanks.

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# Homework Help: Quantum mechanics problem

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