1) Write the differential equation of the radial part. 2) Compute the energy levels and the stationary wave function for = 0 (Use change of rR(r)). [Hint: compare the two derivatives: variable such that U(r) = (²) and (rRni)] 82 ərz r² dr
1) Write the differential equation of the radial part. 2) Compute the energy levels and the stationary wave function for = 0 (Use change of rR(r)). [Hint: compare the two derivatives: variable such that U(r) = (²) and (rRni)] 82 ərz r² dr
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![1) Write the differential equation of the radial part.
2) Compute the energy levels and the stationary wave function for t=0 (Use change of
rR(r)). [Hint: compare the two derivatives:
variable such that U(r)
=
8²
12/12 (²³Rni) and (rRni)]
-2 OR
ər²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67fad71f-33da-4578-b8ac-ddf56bee01b4%2F09bf2f77-0bb6-47b3-9843-34c4990a4a55%2Fa2lmvne_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1) Write the differential equation of the radial part.
2) Compute the energy levels and the stationary wave function for t=0 (Use change of
rR(r)). [Hint: compare the two derivatives:
variable such that U(r)
=
8²
12/12 (²³Rni) and (rRni)]
-2 OR
ər²
Transcribed Image Text:In quantum mechanics we know that when a spherical symmetrical potential V(x,y,z) = V(r)
acts on a particle the angular momentum square operator L² commutes with the Hamiltonian
ħ² 1 a
a
L²
H =
p²
2m
+ V(r) =
+ V(r)
2 mr² Jr (r² = 0 )
2mr²
Note that since the angular dependence is found only in the L², we can separate variables in the
wave function.
Consider a particle in a spherical and infinite potential well:
(0 for 0 ≤rsa
V(r):
{of
loo for
r>a
+
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