I was watching this crash course by Geek Lesson on Quantum Mechanics specifically for Quantum Harmonic Oscillator and [at 1:54:54] when video shows the plot of probability density for different states in Quantum Harmonic Oscillator the probability density is shown more at ends. The speaker gives explanation like this
When something is wiggling in a quantum simple harmonic oscillator it is gonna spin more time in the end, because it is going fast in the middle and slow at the ends. Other thing to notice is that probability density falls off asymptomatically but is never zero for any finite value of x.
Unfortunately, I couldn't understand it. Can someone explain this more clearly ?