In a quantum dot, an electron is trapped in a box whose length is L, and confines the electron between x = 0 and x = L.

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In a quantum dot, an electron is trapped in a box whose length
is L, and confines the electron between x = 0 and x = L.
When the electron make transitions between its energy levels En and
Em, a photon of energy |En−Em| is emitted.
Additionally, we label the ground state as ψ1, with energy E1; the
first excited state as ψ2, with energy E2, and so on.
Answer the following questions:
Sketch the wave function for the ground state and first excited
state.
Calculate the energy levels En.
Find the lowest frequency of emitted light.
If we want to increase the frequency of emitted light by 1%, how
much should we vary the length of the box
(answer in percentage of change)?