Dual nature of matter – Since radiation has dual nature i.e. it possess properties of both; wave and particles and universe is composed of radiation and matter, therefore de-Broglie concluded that the matter must also possess dual nature, since nature loves symmetry.
1) According to De-Broglie, a moving material particle sometimes acts as a wave at some times as a particle or wave is associated with moving material particle which controls the particle in every respect. The wave associated with moving material particle is called matter wave or de-Broglie wave, whose wavelength is given by, λ = h/mv where m is the mass of the particle moving with velocity v and h is Planck’s constant.
2) De-Broglie wavelength associated with electron accelerated under a potential difference V volt is given by λ = 12.27/√V.A
3) The wave centre of electron i.e. de-Broglie hypothesis was established experimentally by Davission and Germer in 1927 for slow electrons and by G.P Thomson for fast electrons.
4) De-Broglie wave is not an electromagnetic wave, but the probability wave.
5) De-Broglie wave length is independent of charges on the moving material particle.
Canonically conjugate quantities
These are those quantities, whose product has the dimension of action, (i.e. energy × time). Its unit is joule-sec). The canonically conjugate quantities are as follow:
1) Energy (E) and time (t)
2) Momentum (p)
3) Position (r)
4) Angular momentum (L)
5) Angular displacement (θ) etc.