1. Density of orbitals in one and two dimensions. (a) Show that the density of orbitals of a free electron in one dimension is D;(e) = (L/n)(2m/h?e};2 . (86) where L is the length of the line. (b) Show that in two dimensions, for a square of area A, Đ2(t) = Am/th? . (87) independent of ɛ.

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1. Density of orbitals in one and two dimensions. (a) Show that the density
of orbitals of a free electron in one dimension is
Đ,(e) = (L/T){2m/h?e}:2 ,
(86)
where L is the length of the line. (b) Show that in two dimensions, for a square
of area A,
Đ2(t) = ,
Am/Th?
(87)
independent of .
Transcribed Image Text:1. Density of orbitals in one and two dimensions. (a) Show that the density of orbitals of a free electron in one dimension is Đ,(e) = (L/T){2m/h?e}:2 , (86) where L is the length of the line. (b) Show that in two dimensions, for a square of area A, Đ2(t) = , Am/Th? (87) independent of .
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