Density of orbitals in one and two dimensions (a) Show that the density of orbitals of a free electron in one dimension is D1() (L ) (2m h2) 2, where L is the length of the line (b) Show that in two dimensions, for a square of area A, Dz() Am h2, Independent of

Question: Density of orbitals in one and two dimensions. (a) Show that the density of orbitals of a free electron in one dimension is D1() =

Density of orbitals in one and two dimensions.
(a) Show that the density of orbitals of a free electron in one dimension is
D1(ε) = (L/π) (2m/h2ε)τ 2,
where L is the length of the line.
(b) Show that in two dimensions, for a square of area A,
Dz(ε) = Am/πh2,
Independent of ε.

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