Question

The volue of
State of a. H-atom in
of normalization constant of ist excited​

Answer 1

Answer:

Explanation:

In the previous lecture we have solved the eigenvalue problem for the hydrogen atom,

Hˆψ(r, θ, ϕ) = Eψ(r, θ, ϕ) (1)

where the Hamiltonian is

Hˆ = −

h¯

2

2µ

∇2 + V (r)

with the reduced mass of the atom

µ = memp/(me + mp)

and the Coulomb potential V (r) = −e

2/r.

We have also seen that the Hamiltonian with a spherically symmetric potential energy function

commutes with the angular momentum operators Lˆ

z and Lˆ2

:

[Lˆ

z, Hˆ ] = 0, [Lˆ2

, Hˆ ] = 0

and of course also [Lˆ

z, Lˆ2

] = 0, and this implies that Hˆ , Lˆ

z and Lˆ2 have common eigen functions,

i.e. that we have also

Lˆ2ψ(r, θ, ϕ) = h¯

2

`(` + 1) ψ(r, θ,