2 A.de Broglie's hypothesis Inspiration:Parallelism between light and matter Wave:frequency ,w,wavelength A,wave vectork..... Particle:velocity v,momentum p,energy c of Yet,tl (corue ture .Matter particles should also posses another side of ture-the wave nature g=hv=hw 卫== A=h/p h/V2mE The state of(micro)-particle should be described by a wave function.Here are some examples of state functions: 1.Free particle of definite momentum and energy is described by a monochromatic traveling wave of definite wave vector and frequency a=cs(红x-2t+0） A'cos(kr-wt+o) =Am(后r-t+0) Replenish an imaginary part 物=A'si血（肛-方t+o we get the final form of wave function =V1+it=A'chevetpe-tu=Aetpre-tet which is the wave picture of free particle.In 3Dwe have 2.Hydrogen atom in the ground state will be shown later to be e-()”- This wave function shows that the motion of electron is in a "standing wave"state.This is the wave picture of above state.2 A. de Broglie’s hypothesis Inspiration: Parallelism between light and matter Wave: frequency ν, ω, wavelength λ, wave vector k · · · · · · Particle: velocity v, momentum p, energy ε · · · · · · • Light is traditionally considered to be a typical case of wave. Yet, it also shows (possesses) a corpuscle nature - light photon. For monochromatic light wave ε = hν = ~ω p = hν c = h λ = ~k, (k = 2π λ ) • Matter particles should also possess another side of nature - the wave nature ε = hν = ~ω p = h λ = ~k This is call de Broglie’s Hypothesis and is verified by all experiments. In the case of non-relativistic theory, the de Broglie wavelength for a free particle with mass m and energy ε is given by λ = h/p = h/√ 2mε The state of (micro)-particle should be described by a wave function. Here are some examples of state functions: 1. Free particle of definite momentum and energy is described by a monochromatic traveling wave of definite wave vector and frequency ψ1 = A ′ cos ( 2π λ x − 2πνt + φ0 ) = A ′ cos (kx − ωt + φ0) = A ′ cos ( 1 ~ px − 1 ~ εt + φ0 ) Replenish an imaginary part ψ2 = A ′ sin ( 1 ~ px − 1 ~ εt + φ0 ) , we get the final form of wave function ψ = ψ1 + iψ2 = A ′ e iφ0 e i ~ pxe − i ~ εt = Ae i ~ pxe − i ~ εt which is the wave picture of motion of a free particle. In 3D we have ψ = Ae i ~ ⃗p·⃗re − i ~ εt 2. Hydrogen atom in the ground state will be shown later to be ψ(r, t) = ( 1 πa3 0 )1/2 e − r a0 e − i ~ E1t This wave function shows that the motion of electron is in a ”standing wave” state. This is the wave picture of above state