Caption: "An animation
showing 3
wave function
solutions to the time-dependent
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 time-dependence)
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
complex-number 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 time-dependent as the
animation shows.
- The stationary states
are called stationary because their
since their QM probabilitiy densities
are time-independent 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 BY-SA 1.0.
Image link: Wikipedia.
File: Quantum file:
qm_harmonic_oscillator_animation.html.