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TRQ7. Solve completely the following Quantum problem. Need full detailed answer, equations and if possible, theory/literature.
Consider N electrons confined to a one-dimensional infinite square
well of length L. Assume N » 1 and ignore the electron-electron
interactions (free electron gas).
(a) Find an expression for the Fermi energy of this system and
express it in terms of the linear electron density (pe = N/L).
(b) Evaluate the total energy and express it in terms of the electron
density pe.
Transcribed Image Text:Consider N electrons confined to a one-dimensional infinite square well of length L. Assume N » 1 and ignore the electron-electron interactions (free electron gas). (a) Find an expression for the Fermi energy of this system and express it in terms of the linear electron density (pe = N/L). (b) Evaluate the total energy and express it in terms of the electron density pe.
Expert Solution
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To find the expression for Fermi  energy and total energy.

Here N-electrons are confined in a 1-D infinite square well with the length L.

 

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