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1. de Broglie's Hypothesis : Matter Waves

1.1. Radiation exhibits particle-like characteristics besides its wave nature

1.2. de Broglie suggested that wave-particle duality is not restricted to radiation but must be universal

1.3. All material particles should display a dual wave-particle behavior

1.4. de Broglie relation λ=h/p, k=p/ℏ

1.4.1. For any material particle with nonzero rest mass

1.4.2. Each particle of momentum p behaves as a group of matter waves with wavelength λ and wave vector k

1.4.3. Governed by speed and mass of the particle

2. Experimental Confirmation of de Broglie's Hypothesis

2.1. Davisson-Germer Experiment

2.1.1. In this experiment, beams of electron strike the nickel crystal's surface and reflected to detectors in such a way that the normal of the crystals bisects the angle between the source of electron beam and detector equally.

2.1.2. It is noticed that the intensity is not same at all angle, at 35 degrees the intensity of electrons detected was lower whereas the intensity at 50 degrees was the maximum.

2.1.3. This phenomenon can be only explained if the electrons were obeying the Bragg’s law of diffraction which suggested that electrons could also behave like wave. Which in fact supports de Broglie’s hypothesis of matter-wave duality. nλ=2dsinθ

2.1.4. The motion of electrons as plane wave is given as Ψ(r ,t)=Ae^i(k ∙r -ωt) =Ae^(i(p ∙r -Et)/ℏ)

2.2. Thomson Experiment

2.2.1. electron were diffracted through a polycrystalline thin film.

2.2.2. diffraction fringes were also observed -this confirm the wave behavior of electron.

3. Matter Waves for Macroscopic Objects

3.1. wavelengths associated with macroscopic sytems are infinitesimally small

3.2. display no discernible wave-like behavior

3.3. to describe the motion of the macroscopic object, geometrical optics should be used.

3.3.1. wave behaves as a ray