Transcription of 1. 2. 3. 磁気回転比 4. 5. スピン角運動量：電子の場合 6. 平行 …
1 zeeman effect . 1. precession . 2.. 3.. 4.. 5.. 6.. 7.. 8.. 9.. 1. Angular momentum . 2. Magnetic dipole moment . 3.. 4.. 5.. 1.. electric field V m electric flux density electric displacement field C m2.. H . magnetic field .. H magnetic H field Am magnetic field intensity B magnetic B field T = Wb m 2. magnetic flux density . 2. precession . v .. 408-11. 1 e m= r1 J ( 1) 1. r dV r v r . 2 2. J ( r1 ) = ev ( r1 r ).. 0 . e L=. r m0 v m = L = L . gyromagnetic ratio . 2m0.. N =m B 2 = L, B 2 =( 0, 0, B2 ).. precession z . L. L. N= = L = ( 0, 0, B2 ). t .. 409-10 . 3.. m0 . e mL. magnetic dipole moment mL =. gL L L. L= L. orbital angular momentum 2m0. e B.. = L g= g ,=. gL 1.. L L. 2m0. e . Bohr magnetron B = 10 24 Am 2 g g-factor 2m0. g . (m L )z =.. Lz L =. = L B Lz m z g L B m . Lg 1. B m z-component .. l . 2l ( l + 1). azimuthal quantum number m l , L2 =. magnetic quantum number 4.. e mS. spin magnetic dipole moment mS =.
2 GS S S. S= . spin angular momentum 2m0. e B gS.. = S g= , gS 2.. S. 2m0. Dirac . g g S = 2 1 + + 2 .. e2 1.. = =. 4 0 c . gS B.. (mS )z = S z = ms S z B g S ms z z-component z-component 1 3 2. ms = , S= s ( s +=. 1). 2 2 ms secondary spin quantum number s spin quantum number 2 4. 5.. Bohr magnetron e . B = 10 24 Am 2 = 10 5 eVT 1 , Am 2 = JT 1. 2m0. z-component e e mL =. gL L L, g L =. L= 1, L =. gL m =1. 2m0 2m0 B. m=0. (m L )z = gL. e Lz B. 2m0 m = 1. e . Lz = m m = m B , m = 0, 1, 2,.. 1. g L =1. 2m0 ms =. 2 B.. e e 1 B. mS =. gs s S, g s 2, s =. S= gs ms = . 2m0 2m0 2. e e 1. (mS )z = gS S z = ms S z . gL 2. 2 ms = 2 m . s B = B , ms = . 2m0 2m0 2. 6.. L. mL = L L N = = m B = L = LB. t e B. = L g= g ,=. gL 1.. L L. 2m0.. S. m s = s S N = =m B = S = s B. t e B. = s g= g , gs 2.. s s 2m0.. S. m p = p S N = =m B = S = p B nuclear magneton t e e . p =g N =g N N , g N , N = 10 27 Am 2. 2m p 2m p 7.. isolated electron.
3 G S S =. mS = B S S g S 2 m S S.. z spin up spin down H int = S S B =. m S B H int = S S z Bz S S . 1. ( 0, 0, S ) , ms = . = S . S z = ms 2. B. ( 0, 0, Bz ) , S =. B= S > 0 .. spin up spin down . 1 1. H int = S ms Bz ms = ms = S = S Bz 2 2. 8.. spin up/ down . S = S Bz 1. ES = . H int . H int S Bz = S. ES = S =. , ms =.. 2 2. g g-factor B . E=. S S B=. z g S B Bz B Am 2 ,[ J ] = [ Nm]. Bz [ T ] = [ N/Am ].. g S B Bz Bz = 2 10 24 =f GHz . h 10 34.. 1. spin up down . 2. z zeeman effect . 3. s . spin up down 501-12 . 1.. 2.. 3.. 4.. 9.. H int = ms s Bz . spin up 1. ms =. 2. ES= S Bz= S.. H int = ms s Bz 1. ms = . 2. spin down z .. e . = s B s = s Bz , s = g s = gs B , gs 2. 2m0 . 10.. Sz z spin up . +. H int = S S B. m S B H int = 2. B 3 .. S =. 0, 0, ( 0, 0, Bz ). , B = 2. 2 2 spin down . 1. =. S S=. S 2 = 2 s ( s + 1) s = S 2 = S x2 + S y2 + S z2. 2 2. up spin . 3 2 . S =. 2. , S x , y = 0, S z = , S z2 = 0. 4 2. 2 2.
4 (S + S ) 2.. 2. x 2. y = S =. 2. 3 4. 11. 2 . z . Lz +1.. + . +. H int = L L B. m L B H int = 2. 0 0. B.. L 1 =. 0, 0, , L0 = ( 0, 0, Bz ). 0, B = . 2 2 -1.. =. L L=. L2 = 2l ( l + 1) l = 1 L2 = L2x + L2y + L2z +1 1 . 1 L2 1 = 2 2 , 1 Lx , y 1 = 0, 1 Lz 1 = , 1 L2z 1 = 0. 4 2. 1 ( L + L=. ) 1 3 1 L=. 2 2 2 2.. x y 1. 3. 12.. 1. m B 2 = . 0 B ( r ) B ( r ) dV. 1 2 = J1 ( r ) A 2 ( r ) dV.. 1. m B 2 =. 0 B ( r ) B ( r ) dV. 1 2 .. 1. z . 2.. 3.. Bz g g-factor spin up zeeman splitting 1. ms =. 2. ES = S = g S B Bz . 1. ms = . 2 .. spin down Electron Spin Resonance ES . 13.. s spin quantum number .. spin angular momentum =S z ms , =. ms s 1 S = S Bz 2. e . ES g S =. = B Bz , gS 2 = gS. 2m0. Normal zeeman effect .. l = 1 . =Lz m , m l .. l . magnetic quantum number azimuthal quantum number Bz . m =1. EL g L =. = EL. B Bz . m=0. EL. L = L Bz m = 1.. e e = L g L =1. g L . 2m0 2m0 14.. v . r m0. dv = m 02r ev B B = ( 0, 0, Bz ).
5 Dt .. 0. 1. 0 x . 2. 0 . 3.. 4.. 5.. 6. p. 16 . x ( t ) x= y ( t ) y0 sin t . = 0 cos t , d 2x m0 2 = m 02 x eBz dy z ( t ) = 0 cos 0t dt dt d2y dx 0 . m0 2 = m 02 y + eBz dt dt d 2z m0 ( 02 2 ) x0 =. e Bz y0. m0 2 = m 02 z m0 ( 02 2 ) y0 =.. dt e Bz x0. 15.. electric dipole radiation . 1.. 2.. 3.. 4.. x ( t ) = cos t , y ( t ) = sin t + . 2. eBz eBz . =. + 0 + . 2 .. 2m0 0 . 2 m . 1.. 2.. 0 m = 1.. x . x ( t ) =. cos t , z ( t ) 0 cos 0t . 1. 0. m = 0, 1 B = ( 0, 0, Bz ). 2.. 16.. m . z y . P l =1 m = 1, +. m = 0, 0 2 EL. m = 1, . z .. m=0. S l =0 m = 1 m = 0, 1 .. 1.. eBz 2 EL = . e 2.. + =. = E=. L Bz 3. 4.. m0 2m0. Bohr magnetron e e . EL g L B Bz . = g L =1. =. EL Bz B . 2m0 2m0 17.. Selection rule LS coupling =. s 0, m=. S 0 . spherical harmonics Yml ( , ) L2 Yml = 2l ( l + 1) Yml r = z rY01 ( ) r cos z = ( 0, 0,1). l ', m ' z l , m l ', m ' rY01 l , m P l =1 . z .. y . m . (Y )Y Y m =1. *. l'. m'. 1 l 0 m sin d d 0.
6 M=0. l = 1, m = 0. m = 1. Fermi's golden rule . z .. R. Loudon, The Quantum Theory of Light, , Oxford 2 . ( ). 2. Ti f = f H'i m=0. 2. 2 S l =0. l = 0, m = 0 z l = 1, m = 0 . 18.. y r = x iy rY 11 ( , ) . = (1, i, 0 ). l ', m ' x iy l , m (Yml '' ) Y 11 Yml sin d d 0 l = 1, m = 1. *. l ', m ' x l , m l = 1, m = 1 = (1, 0, 0 ). l ', m ' y l , m l = 1, m = 1 = ( 0,1, 0 ).. z y . P l =1 m =1. m=0. m = 1.. m=0. S l =0 m = 1 m = 0, 1 19.
