1.Free particle of definite momentum and energy is described by a monochromatic trav- eling wave of definite wave vector and frequency =cs(臣-2an+） =A'cos (kx-wt+po) =cs(房r-方t+o） Replenish an imaginary part 约=sm(r-方t+0) we get the final form of wave function 少=十i的=A'cipe严e-et=Aeipre-te which is the wave picture of motion of a free particle.In 3D we have =Aetfre-fet 2.Hydrogen atom in the ground state will be shown later to be 9-() ee-t This wave function shows that the motion of electron is in a"standing wave"state This is the wave picture of above state. B.Stationary Schrodinger equation The parallelism between light and matter can go further Light: wave nature omitted geometric optics wave nature can not be omitted wave optics Matter: wave nature omitted particle dynamics a new mechanics. wave nature can not be omitted namely quantum mechanics Particle Dynamics←→Geometric Optics 业 Quantum Mechanics←凸Wave Optics 1. Free particle of definite momentum and energy is described by a monochromatic trav￾eling wave of definite wave vector and frequency ψ1 = A 0 cos µ 2π λ x − 2πνt + ϕ0 ¶ = A 0 cos (kx − ωt + ϕ0) = A 0 cos µ 1 ~ px − 1 ~ εt + ϕ0 ¶ Replenish an imaginary part ψ2 = A 0 sin µ 1 ~ px − 1 ~ εt + ϕ0 ¶ , we get the final form of wave function ψ = ψ1 + iψ2 = A 0 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) = µ 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. B. Stationary Schr¨odinger equation The parallelism between light and matter can go further Light: wave nature omitted geometric optics wave nature can not be omitted wave optics Matter: wave nature omitted particle dynamics wave nature can not be omitted a new mechanics, namely quantum mechanics Particle Dynamics ⇐⇒ Geometric Optics ⇓ ⇓ Quantum Mechanics ? ⇐⇒ Wave Optics 4