Question 5 The eigenfunction for the ground state of the hydrogen atom has the form ₁(r) = N₁e-¹/ where ao is the Bohr radius, N₁ is a constant and is the radial distance of the electron from the nucleus. 47²dr =1 find the constant N₁. a) By normalizing the integral in accordance with [|₁ (~^)² 477- b) Given that the eigenfunction of an excited state has the form ₂ (r) = N₂₁ (1+r)e¯¹/2, use the orthogonality condition for 1 and 2 to find the constant λ and sketch the eigenfunction ()

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Question 5
The eigenfunction for the ground state of the hydrogen atom has the form
₁(r) = N₁e-¹/
where ao is the Bohr radius, N₁ is a constant and is the radial distance of the electron from the nucleus.
a) By normalizing the integral in accordance with [|₁ (-)² 470³²dr = 1 find the constant N₁.
b) Given that the eigenfunction of an excited state has the form ₂(¹) = N₂ (¹+r)e¯¹/2, use the
orthogonality condition for and 2 to find the constant λ and sketch the eigenfunction ()
Transcribed Image Text:Question 5 The eigenfunction for the ground state of the hydrogen atom has the form ₁(r) = N₁e-¹/ where ao is the Bohr radius, N₁ is a constant and is the radial distance of the electron from the nucleus. a) By normalizing the integral in accordance with [|₁ (-)² 470³²dr = 1 find the constant N₁. b) Given that the eigenfunction of an excited state has the form ₂(¹) = N₂ (¹+r)e¯¹/2, use the orthogonality condition for and 2 to find the constant λ and sketch the eigenfunction ()
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