メゾスコピック： 何が面白いの？ - 家研究室 - 東京大学

20051121

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20051121

3 6 12 18 24 2800k

-12 -9 -6 -3 O-157 -35 -32 -21 -18

CD-ROM/DVD

GPSGrobalGrobal Positioning System)GPS

CCD

MRI MEG SQUID (

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Matter Material mattermaterial(space-time) Solid State Physics (Condensed Matter PhysicsMaterials Science

Curiosity-Driven Research (Mission-Oriented Research

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(reductionism) (emergent properties) More is different.(P.W.Anderson)

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kg100.91C101.603019−−×=×=m eeenpmmm 1840≈≈sJ106.6234⋅×=−hhν

e = 1.6×101 eV = 1.6×10−19−19CJJ = kg m2 s 21 mv22h==6.62×104.13×10−34−15J ⋅seV ⋅seVhν= 1 eV ↔ ν =↔ν= 8070 cmc-12.42×1014Hz↔ λ = 1240 nm

sJ101.05234⋅×==−πhh222222222),,(),,()(2zyxzyxEzyxrVm∂∂+∂∂+∂∂≡∇=⎟⎟⎠⎞⎜⎜⎝⎛+∇−ψψh),,( zyxψE2),,( zyxψ

⎡⎢− h⎣22∇ −2m0a+e -e2e ⎤⎥ψ( r)4πεr ⎦4πε0h= me220=⎛ 1 ⎞Ry =⎜4⎟⎝ πε0 ⎠2= Eψ( r)0.053nmme2h42= 13.6 eV0RyEn=1n=2V ( r)n=32e= −4πε 1E n= − Ry2nr n= n 2 a00r

hν⎟ ⎠ ⎞⎜⎝⎛−=−=2211nmRyEEhmnν2nRyE n−=Hz104.5514×=ν= 659 nmλ1.89 eV365312122==⎟⎠⎞⎜⎝⎛−=−RyRyEEmn(m=2)

0214412sdpfE (eV)1s2s2p3s 3p 3d4f4d4p4s222222222),,(),,()(2zyxzyxzyxrVm∂∂+∂∂+∂∂≡∇=⎟⎟⎠⎞⎜⎜⎝⎛+∇−ψεψh),()(),,( φθφθψYrRr =22222222sin1sinsin11φθθθθθ∂∂⎟ +⎠⎞⎜⎝⎛∂∂∂∂⎟ +⎠⎞⎜⎝⎛∂∂∂∂≡∇rrrrrrm=-2m=0m=1m=-1m=2m=-3m=3))exp((cos),( φθφθimPYmlml∝1)(21,,,2,0,1,+−= −=llllmlLLL, +1,= lln,σ,, mln 1= ±σ

Ymlm( θ , φ)∝ P (cosθ)exp( imφ)ls p xp y p zd yzd zxd xy d x 2-y2d 3z 2-r2

+ZeZ n, l, m,-e+Ze-e-e-eNa Z=11Na:(1s)2(2s)2(2p)6(3s)1

7s6s5s6p5p5d4d4f4s4p3d3s2s3p2pHLi BeB C N O F NeNaMgAl Si P S Cl ArK Ca Sc Ti V Cr MnFeCo Ni Cu ZnGaGeGe AsSe Br KrRbHeSr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I XeCs Ba La Hf Ta W Re Os Ir Pr Au Hg Tl Pb Bi Po At RnFrRaAcRu HaCePr Nd Pm Sm Eu Gd Tb Dy Ho ErTmYbLu1sThPa U Np Pu Am Cm Bk Cf Es FmMdNoLw

n, l, m,n ()n=1 21 = 2n=2 2(1+3) = 8n=3 2(1+3+5) =181 2,10,18,36He, Ne, ArKrXe

ZeV eVmeV1.5V V 1.5eV 2.5eV

C 60C 70

NaClPb 1-x Sn x

T= 0 T > T c

(T > 0 E S F = E−TSF=E−TS

TT k BkB= 1.38×10−23J/KkB T = 1 eV ↔ T = 11600 KT= 300 K ↔ kB T =25 meV

74%hcp

θd sinθ = nλ0.3 nm X

θ2θdθ2d sinθ = nλX

NeArKr, Xe ()He

HHeLi Be B C N O F NeNa +Na Mg Al Si P S Cl ArCl − K Ca Ga Ge As Se Br KrCsCl

Na:(1s)2(2s)+ ++ ++ ++ +Na +2(2 p)-e6+ ++ ++ ++ +(3s)1HLi Be B C N O F NeNa Mg Al Si P S Cl ArKHeCa Ga Ge As Se Br Kr

-e H 2+e+e-e+e +e+e +e

CSiGeHHeLi Be B C N O F NeNa Mg Al Si P S Cl ArK Ca Ga Ge As Se Br Kr

DNA

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