I actually want to know can quantum mechanics discuss the wave nature of the dual particle nature in detail.
Yes. The second quantization procedure, in effect, elucidates particle nature of the Maxwell equations.
Source: any sufficiently detailed textbook on quantum electrodynamics.
The classical wave equation doesn't have anything to do with the wave/particle duality of non-relativistic quantum mechanics, however. So the answer to the question, as posed, is negative.
Dear Saswata,
Nor I believe in wave/particle duality! What does one mean by this duality? The better question may run as follows: Is particle=wave? No!
However, what do you mean by classical wave? Please describe it concisely. Thanks for your description! Marc.
There are essentially semi-classical effects built into E & M, like evanescence. This is essentially quantum mechanical tunneling but with photons instead of massive particles, however the effect does not require second quantization to explain, only Maxwell's equations.
I am not quite sure what the question means. The most obvious answer is the de Broglie wave equation links the classical concept of particle momentum with a wave length, from which you can predict how to make the two-slit experiment work with C 60 molecules. On a lesser note, in chemistry I have shown how you can use this equation to predict reasonably accurately the average bond lengths in aromatic molecules based on the number of canonical structures. The effect is real, but I am not sure this is what you are asking.
Dear Ian,
If 'a' wave has length then it is logically limited (cf. 'a' and 'length'). Is wave by nature limited logically speaking?
Dear Saswata,
it is well-known that Hamilton gave classical mechanics the logical structure of geometrical optics (in short: Hamilton-Jacobi equation in mechanics corresponds to the eikonal equation in ray optics) and that Schrödingers main intuition was to go the way in the opposite direction: to transform trajectory (=ray) mechanics into a wave mechanics. In mathematics it is common to associate characteristic curves with hyperbolic differential equations (e.g. wave equation) and to use these (you have to solve 'only' ordinary differential equations to get them) to construct the solution of the partial differential equation. Ironically most authors of textbooks on partial differential equations seem not to know that in physics the reverse method is more successful: to find particle trajectories from the partial differential equation of Hamilton and Jacobi.
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