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.)


  1. The capital Greek letter Ψ (pronounced and named Psi) is the common symbol for the wave function.

  2. 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.

  3. The full wave function is always time-dependent as the animation shows.

  4. The stationary states are called stationary because their since their QM probabilitiy densities are time-independent as the animation shows.

  5. 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.