WOLFRAM|DEMONSTRATIONS PROJECT

Time-Dependent Superposition of Rigid Rotor Eigenstates

​
expansion coefficients
SubscriptBox[\(c\), \(0, 0\)]​
1.
SubscriptBox[\(c\), \(0, 0\)]​
0.
SubscriptBox[\(c\), \(1, 0\)]​
0.
SubscriptBox[\(c\), \(1, 1\)]​
0.
SubscriptBox[\(c\), \(2, \(-2\)\)]​
0.
SubscriptBox[\(c\), \(2, \(-1\)\)]​
0.
SubscriptBox[\(c\), \(2, 0\)]​
0.
SubscriptBox[\(c\), \(2, 1\)]​
0.
SubscriptBox[\(c\), \(2, 2\)]​
0.
time
0.
This Demonstration looks at a time-dependent superposition of the nine lowest quantum rigid-rotor eigenstates,
ψ(θ,ϕ)=
2
∑
J=0
J
∑
M=-J
c
J,M
-
E
J
t/ℏ

M
Y
J
(θ,ϕ)
, where
M
Y
J
(θ,ϕ)=
(2J+l)
4π
(J-M)!
(J+M)!
M
P
J
(cosθ)
Mϕ
e
,
M
P
J
are the associated Legendre polynomials, and
J
and
M
are the orbital and magnetic quantum numbers, respectively. The energy levels are
E
J
=J(J+1)
B
, where
B
≡
h
8
2
π
Ic
is the rotational constant. The figure shows the complex wavefunction
ψ(θ,ϕ)
, where the shape is its modulus and the coloring is according to its argument, the range
0
to
2π
corresponding to colors from red to magenta.