Quantum Mechanics Equations and Concepts, Study notes of Physical Chemistry

Download Quantum Mechanics Equations and Concepts and more Study notes Physical Chemistry in PDF only on Docsity! 1 Equation list: p = h / λ, ε = h ν, E = n h ν, ν = c / λ, p = m v (m ≠ 0), KE = ½ m v2 = h ν - I0 ∆x ∆p ≥ ½ ħ; ∆t ∆E ≥ ½ ħ <Â> = ∫ Φ* Â Φ dτ, Â Φ = a Φ, ipx −=ˆ ħ dx d , iJ z −=ˆ ħ ϕd d Hermitian: ∫ Φ* Â Ψ dτ = ∫ Ψ Â* Φ* dτ Commutator: [Â, Ĉ] =  Ĉ - Ĉ  ĤΨ (r) = EΨ (r) ∫ Φ1* Φ2 dτ = δ12, δ12 = 0 (when 1 ≠ 2), or 1 (when 1 = 2) )( 2 ˆ 2 2 2 2 2 22 zyxm H ∂ ∂ + ∂ ∂ + ∂ ∂ −= h , )( 8 2 2 3 2 2 2 2 2 1 2 ,, 321 zyx nnn L n L n L n m hE ++= , )sin()sin()sin(8 321,, 321 zyxzyx nnn L zn L yn L xn LLL πππψ = , n1, n2, n3 =1, 2, …… 22 22 2 1 2m ˆ kx dx dH +−= h , ωh)2/1( += vEv , m k =ω , 2 )( yvvv eyHN −=ψ , xy ∝ I J d dH z 2 ˆ 2I ˆ 2 2 22 =−= ϕ h , 2rI µ= , 2I 22hmEm = , ϕ π ψ imm e2 1 = , m = 0, ±1, … I JH 2 ˆˆ 2 = , 2I )1( 2h+ = llEl , ϕθ immll ePN )(cosY ,ml, = , l = 0, 1, …; m = 0, …±l Ĵ2Yl,m = l(l+1) ħ2 Yl,m, Ĵz Yl,m = m ħ Yl,m r Ze m H 0 2 2 2 42 ˆ πε −∇−= h , 2 2 n IZEn −= , n = 1, 2, …, I = 13.6 eV, 1 eV = 1.6×10 -19 J mllnmln YrR ,,,, )(=Ψ , ρρρ −= eLNR ln l lnln )(,,, , n Zr ∝ρ ∆E = hν