Probability density and acceleration

[Jarvis323]

In class we went over the probability density for an object on a pendulum, and how at the lowest energy states, you would have strange distributions such as the object being more likely to be found at the bottom. But as you increase the energy level, the wave equation becomes more and more like how you would expect, as the frequency of the probability wave gets higher, and the sides taper up.

But even in very high states, you still have these "oscillations" in probability of the object being in a given place along the path the pendulum swings, even though the oscillations might be very closely spaced.

I was wondering if this means anything in terms of how the object moves or accelerates through space? If you can have these very high frequency oscillations of probability density along an objects trajectory, does this mean that the object is not moving "smoothly" through space? For example instead of moving continuously, at the lowest levels it's actually making incremental bursts forward, or something of that sort?

 

[Simon Bridge]

What do you mean "an object on a pendulum"?
Do you mean you have been solving the Schrödinger equation for the harmonic oscillator potential?

If so, then the wavefunctions you found are for stationary states - i.e. there is an important sense that they represent something "not moving".

Individual eigenstates do not correspond to any intuition drawn from classical behavior.

The classical behavior of the particle is given by the expectation value of the wavefunction.

Work a superposition of, say, the first two, and you'll see what happens.