Consider a system of five noninteracting electrons (in the approximation where the Coulomb interaction between the electrons is neglected) that are confined to move in a common onedimensional infinite potential well of length \( L=0.5 \mathrm{~nm}: V(x)=0 \) for \( 0<x<L \) and \( V(x)=\infty \) for other values of \( x \). (a) Find the ground state energy of the system. (b) Find the energy of the first state of the system. (c) Find the excitation energy of the first excited state.
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The energy levels are given by: \[ E_n = \frac{n^2 h^2}{8mL^2} \] where \( n \) is the quantum number, \( h \) is Planck's constant, \( m \) is the mass of the electron, and \( L \) is the length of the well. Show more…
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