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Multiple choice
When the 3D Schrodinger equation for a central potential is separated as
ψ
=
R
(
r
)
Y
(
θ
,
ϕ
)
\psi = R(r)\,Y(\theta,\phi)
ψ
=
R
(
r
)
Y
(
θ
,
ϕ
)
, the azimuthal equation gives
Φ
(
ϕ
)
=
exp
(
i
m
ℓ
ϕ
)
\Phi(\phi) = \exp(i\,m_\ell\,\phi)
Φ
(
ϕ
)
=
exp
(
i
m
ℓ
ϕ
)
. What physical requirement forces
m
ℓ
m_\ell
m
ℓ
to be an integer?
Normalization of the radial function
R
(
r
)
R(r)
R
(
r
)
at the origin
The requirement that the energy be negative for a bound state
Single-valuedness of the wavefunction:
Φ
(
ϕ
+
2
π
)
\Phi(\phi + 2\pi)
Φ
(
ϕ
+
2
π
)
must equal
Φ
(
ϕ
)
\Phi(\phi)
Φ
(
ϕ
)
The Pauli exclusion principle applied to the angular coordinate
Check answer