|q⟩
Bad Qubits
Play
Quest
Questions
Learn
Playground
☕
← Question Bank
Multiple choice
For the hydrogen radial equation written with the reduced radial function
u
(
r
)
=
r
R
(
r
)
u(r) = r R(r)
u
(
r
)
=
r
R
(
r
)
, the effective potential is
V
e
f
f
(
r
)
=
−
e
2
/
(
4
π
ϵ
0
r
)
+
ℏ
2
ℓ
(
ℓ
+
1
)
/
(
2
μ
r
2
)
V_{eff}(r) = -e^2/(4\pi\epsilon_0 r) + \hbar^2 \ell(\ell+1)/(2\mu r^2)
V
e
f
f
(
r
)
=
−
e
2
/
(
4
π
ϵ
0
r
)
+
ℏ
2
ℓ
(
ℓ
+
1
)
/
(
2
μ
r
2
)
. What is the role of the second term?
It is a repulsive centrifugal barrier that grows as
1
/
r
2
1/r^2
1/
r
2
and pushes the electron away from the origin for
ℓ
>
0
\ell > 0
ℓ
>
0
It is the kinetic energy of the center-of-mass motion
It is an additional attractive term that deepens the Coulomb well for all
ℓ
\ell
ℓ
It is a constant energy offset independent of
r
r
r
and
ℓ
\ell
ℓ
Check answer