# 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