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