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I'm doing a project with lead (II) sulfide quantum dots because they have optical transitions in the near infrared. I understand the simple "particle in a box" approach where confinement strengthens exponentially when the box shrinks.

What I don't get is how this confinement results in discrete energy levels? Can someone tell me how this shrinking of molecular size and confinement of the electron hole pair (exciton Bohr radius) results in discrete energy levels? Is it the electron shells being changed?

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