I am reading some materials on quantum mechanics. I am a bit confusing in the chapter on wave-particle duality and following questions arise
In classical mechanics, the force a particle experience is the gradient of the potential. If a particle is in a potential of form $\sin(x)$ where $x$ is the spatial variable, the gradient of the potential is still of sinusoidal form so the particle is experiencing a force back and forward like pendulum, right? So if we consider the particle quantum mechanically, the potential is still of the form $\sin(x)$ so what can we tell about the force that particle experiencing?
In a online material, when talking about the zero-point energy, it said if the temperature is extremely low (close to absolute zero kelvin), all bosonic atoms are staying in the lowest state, so it just like a big atom with wave function in the form of plane wave. If that's true, I am wondering how that "plane wave" will react to the potential of $\sin(x)$, will it see a net force or zero force? Why?