Caption: "An animation
showing 3
wave function
solutions to the timedependent
Schroedinger equation
of quantum mechanics
for a
quantum harmonic oscillator
(the analog
to the harmonic oscillator
of classical physics).
Left:
The real part
(blue)
and imaginary part
(red) of the
wave function.
Right: The
QM probabilitiy density
for the particle.
The top two rows are the lowest
two stationary states (energy eigenstates plus timedependence)
and
the bottom is the superposition state Ψ_N = (Ψ_0+Ψ_1)/sqrt(2),
which is NOTt a
stationary state." (Slightly edited.)
Features:
 The capital Greek letter Ψ
(pronounced
and named Psi) is the
common symbol
for the wave function.
 The QM probabilitiy density ρ which
is equal to the square of the
complexnumber absolute value
of the wave function: i.e., ρ = Ψ**2.
The QM probabilitiy density is, among other things,
the probability density
for measuring a particle at any point in space.

The full wave function
is always timedependent as the
animation shows.
 The stationary states
are called stationary because their
since their QM probabilitiy densities
are timeindependent as the
animation shows.
 The superposition state is NOT a
stationary state,
and hence its QM probabilitiy density varies in time.
Credit/Permission: ©
Steve Byrnes (AKA User:Sbyrnes321),
2011 /
Creative Commons
CC BYSA 1.0.
Image link: Wikipedia.
File: Quantum file:
qm_harmonic_oscillator_animation.html.