How can a single particle be a wave?
Always thought wave is defined as back-and-forth motion for single particle, or we have many particles, wave should be as passing energy from one particle to another where we might have longitudinal or transverse. In which cases, from classical wave definition, each particle moves - right and left - or - up and down.
Schrodinger, when he was trying to come up with differential, he already assumed that particle is a wave and used Einstein-de Broglie's postulates to derive it for single, freely moving particle. While his derivation is clear, I don't get how a single particle be called a wave. Since schrodinger derived it for freely moving, he first assumed no force was acting on it, and if no force acting on it, particle actually just keeps going and doesn't get back and forth motion.
- So in case of deriving it for freely moving particle, why did he assume it would have $\cos$ form, because if it does so, particle must be moving back and forth as we have on $\sin$ or $\cos$ graph, but if no force acting on it (I'm emphasizing this because thats how he derived his equation to get $V_0(potential)$ constant), it should move forward.
Note that I'm only talking about a single particle (which is said to have wave properties as well).
