Do strings themselves exhibit wave/particle duality?
An object in quantum mechanics has the following description: when localized perfectly it is either located at a point, in which case it is a "point particle", or an extended object, located at a line of points, a 2D surface of points, etc. If you do not localize the object, it becomes 'fuzzy' in the sense that it is not longer located at a particular point in space, or a line of points, or a 2D surface of points, etc; but we still say the objects are point particles or strings or membranes, etc. The wave behavior of these objects is in the sense that in interacting with another object of its type, like scattering, its interaction is characterized by interference (constructive and destructive, with points in between). I have kept the discussion general, allowing 0D, 1D, 2D,... objects, so in the sense described above (in the same sense as point particles) strings have a "wave nature".
Keep in mind when interpreting objects as being "wavelike" that they are really described by complex waves in quantum mechanics, so the situation is not the same as having real waves interacting. In fact, one can treat the situation by drawing the objects (say point particles) taking all possible paths or all possible ways of scattering off another similar object and using the "almost least action principle", which relegates the wavelike nature to the way we compute physical processes (this is the essence of the path integral formulation of quantum mechanics in which Feynman thought of particles as individual point objects taking all configurations possible; quantum field theory takes a different interpretation, that we should do away with the notion of particles as absolute entities taking up points in space that take all possible paths...in fact, the notion of a particle further loses its old meaning in qauntum field theory in *curved* spacetimes).
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