[물리] 속이 텅 빈 구 속의 전자 (MIT)
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An electron is confined to the interior of a hollow spherical cavity of radius R with impenetrable walls. Find an expression for the pressure exerted on the walls of the cavity by the electron in its gorund state.
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For the ground state, l = 0, and if we set the radial wave function as R(r) = χ(r)/r, then χ(r) is given by
where μ is the electron rest mass. R(r) is finite at r = 0, so that χ(0).
The solutions satisfying this conditions are
for which
The average force F acting radially on the walls by electron is given by
As the electron is in the ground state, n = 1 and
The pressure exerted on the wall is
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