EDMAR G. PANTOHAN
This report is based on the very interesting researches of L. de Broglie on what he called “phase waves”. The advantages of the wave theory,
- The laws of motion and quantum condition can be derived from Hamiltonian principle.
- The discrepancy between the frequency of motion and frequency of emission disappears when the latter frequencies coincide with the difference of the former.
- It possible to pursue the so called transitions.
- This wave theory is better supported by experiment
Consider a point mass m moving in a conservative field of force in q-space. Using the well known Hamiltonian principle and the kinetic energy of the particle, we can have the Hamiltonian partial differential equation. To solve this equation we put W=Et+S(x,y,z), geometrically we described W as a system of surfaces. By allowing this to vary with time, the phase velocity u of the wave is solve. But this velocity u is not the velocity of the particle which proportional to the square root of the difference between energy and potential.
Though in the above we are dealing with wave surfaces and calculating phase velocity, the whole established analogy is more on geometrical optics than real physical or undulatory optics. The fundamental mechanical conception is that of the path or the orbit of the particle and it corresponds to the conception of rays in optical analogy. But the concept of rays loses its significance in real physical optics as soon as the dimensions of the beam or of material become comparable with the wavelength . Considering this striking fact, the ordinary mechanics is really not applicable to mechanical system of a very small atomic dimensions. The same kind as the non-applicability of geometrical optics to the phenomena of diffraction or interference.