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4%,1+,%)#*',5)"1#6"#$%$"&'#()&*')+,"#7#8N9# !>%0*1/'",1#$%$"&'#()&*')+,"#

!L = !r ! !p (1)

H"(r,#) = $(r,#) H"(r,# + #0) = $(r,# + #0) (2)

R(#0)"(r,#) = "(r,# + #0) (3)

HR = RH (4)

#0 (5)

(x, y, z) (6)

(x cos #0 + y sin #0 , "x sin#0 + y cos #0 , z) (7)

[Rz(#0)"](x, y, z) = "(x cos #0 + y sin#0 , "x sin#0 + y cos #0 , z) (8)

#0 #0 # 1 (9)

[Rz(#0)"](x, y, z) $ "(x, y, z) + #0

!y%"

%x" x

%"

%y

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Rz(#0) $ 1" i#0

hLz (11)

Lx, Ly, Lz (12)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (13)

{H, Lx} {H, Ly} {H, Lz} (14)

{H, Lx, Ly, Lz} (15)

" $ (16)

4/1')(,6"#0%&(',"66"#H#$%$"&'#()&*')+,"#"&#$*(/&)+,"#(6/;;)+,"##

O*E)&)')%&#+,/&')+,"#E%1$"66"$"&'#)5"&')+,"#H#%0*1/'",1#C#'1%);#(%$0%;/&'";##

PQRQ#G&#;>)&'*1";;"#)()#/,#$%$"&'#()&*')+,"#ST%1<)'/6TU#0%,1#6/#0/1')(,6"##

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V(')%&#;,1#,&"#E%&(')%&#5>%&5"##################7##G&#;/)'#+,"#################I#5%&(#H#

!L = !r ! !p (1)

!p =h

i!" (2)

H"(r,#) = $(r,#) H"(r,# + #0) = $(r,# + #0) (3)

R(#0)"(r,#) = "(r,# + #0) (4)

HR = RH (5)

#0 (6)

(x, y, z) (7)

(x cos #0 + y sin #0 , #x sin#0 + y cos #0 , z) (8)

[Rz(#0)"](x, y, z) = "(x cos #0 + y sin#0 , #x sin#0 + y cos #0 , z) (9)

#0 #0 $ 1 (10)

[Rz(#0)"](x, y, z) % "(x, y, z) + #0

!y%"

%x# x

%"

%y

"(11)

Rz(#0) % 1# i#0

hLz (12)

Lx, Ly, Lz (13)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (14)

{H, Lx} {H, Ly} {H, Lz} (15)

{H, Lx, Ly, Lz} (16)

" $ (17)

!L = !r ! !p (1)

!p =h

i!" (2)

"(x, y, z) (3)

H"(r,#) = $(r,#) H"(r,# + #0) = $(r,# + #0) (4)

R(#0)"(r,#) = "(r,# + #0) (5)

HR = RH (6)

#0 (7)

(x, y, z) (8)



#0 #0 $ 1 (11)

[Rz(#0)"](x, y, z) % "(x, y, z) + #0

!y%"

%x# x

%"

%y

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Rz(#0) % 1# i#0

hLz (13)

Lx, Ly, Lz (14)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (15)

{H, Lx} {H, Ly} {H, Lz} (16)

{H, Lx, Ly, Lz} (17)

" $ (18)

"'#5"#$W$"#0%,1##Lx, Ly (1)

!0 ! 1 (2)

[Rz(!0)"](x, y, z) " "(x + !0y , #!0x + y , z) (3)

y! " #!0x + y (4)

x! " x + !0y (5)

#L = #r $ #p (6)

#p =h

i#% (7)

"(x, y, z) (8)

H"(r,!) = $(r,!) H"(r,! + !0) = $(r,! + !0) (9)

R(!0)"(r,!) = "(r,! + !0) (10)

HR = RH (11)

!0 (12)

(x, y, z) (13)

(x cos !0 + y sin !0 , #x sin!0 + y cos !0 , z) (14)

(x!, y!, z!) (15)

x! = x cos !0 + y sin !0 (16)

y! = #x sin!0 + y cos !0 (17)

z! = z (18)

2Q#

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6>%0*1/'",1#1%'/')%&###########5>,&#/&@6"#####/,'%,1#5>,&#/A"######5%&&*#H!(r,") = #(r,") H!(r," + "0) = #(r," + "0) (1)

R("0)!(r,") = !(r," + "0) (2)

HR = RH (3)#####";'#)&B/1)/&'#0/1#1%'/')%&#;)#

H!(r,") = #(r,") H!(r," + "0) = #(r," + "0) (1)

R("0)!(r,") = !(r," + "0) (2)

HR = RH (3)

[A"$06"#H#1%'/')%&#/,'%,1#5"#6>/A"#z#8(%%15%&&*";#0%6/)1";#C#NO9#

!L = !r ! !p (1)

!p =h

i!" (2)

"(x, y, z) (3)

H"(r,#) = $(r,#) H"(r,# + #0) = $(r,# + #0) (4)

R(#0)"(r,#) = "(r,# + #0) (5)

HR = RH (6)

#0 (7)

(x, y, z) (8)



#0 #0 $ 1 (11)

[Rz(#0)"](x, y, z) % "(x, y, z) + #0

!y%"

%x# x

%"

%y

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Rz(#0) % 1# i#0

hLz (13)

Lx, Ly, Lz (14)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (15)

{H, Lx} {H, Ly} {H, Lz} (16)

{H, Lx, Ly, Lz} (17)

" $ (18)

V (r) = ! q2

4!"0r

!

x

y

!tournee(r,") = [Rz,!!] (r,") = !(r,"! #)

R!u," !u

!

G0*1/'",1#1%'/')%&#/,'%,1#5"#G\#8(%%15%&&*";#(/1'*;)"&&";9#

:%'/')%&#5>,&#/&@6"#####/,'%,1#5"#6>/A"#G\#H#

y

x

H!(r,") = #(r,") H!(r," + "0) = #(r," + "0) (1)

R("0)!(r,") = !(r," + "0) (2)

HR = RH (3)

"0 (4)

(x, y, z) (5)

(x cos "0 + y sin "0 , !x sin"0 + y cos "0 , z) (6)

[Rz("0)!](x, y, z) = !(x cos "0 + y sin"0 , !x sin"0 + y cos "0 , z) (7)

"0 "0 " 1 (8)

[Rz("0)!](x, y, z) # !(x, y, z) + "0

!y$!

$x! x

$!

$y

"(9)

Rz("0) # 1! i"0

hLz (10)

Lx, Ly, Lz (11)

!L = !r ! !p (1)

!p =h

i!" (2)

"(x, y, z) (3)

H"(r,#) = $(r,#) H"(r,# + #0) = $(r,# + #0) (4)

R(#0)"(r,#) = "(r,# + #0) (5)

HR = RH (6)

#0 (7)

(x, y, z) (8)


(x!, y!, z!) (10)


#0 #0 $ 1 (12)

[Rz(#0)"](x, y, z) % "(x, y, z) + #0

!y%"

%x# x

%"

%y

"(13)

Rz(#0) % 1# i#0

hLz (14)

Lx, Ly, Lz (15)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (16)

{H, Lx} {H, Ly} {H, Lz} (17)

{H, Lx, Ly, Lz} (18)

!

!

x! = x cos ! + y sin !

y! = !x sin ! + y cos !

= !(x cos " + y sin " , !x sin" + y cos " , z)

!tournee(x, y, z) =

z! = z

[Rz,!!] (x, y, z) = !(x!, y!, z!)

(>";']C]5)1"#H#

H#@*&*1/'",1;#)&E)&)'*;)$/,A#5,#@1%,0"#5";#1%'/')%&;#

H!(r,") = #(r,") H!(r," + "0) = #(r," + "0) (1)

R("0)!(r,") = !(r," + "0) (2)

HR = RH (3)

"0 (4)

(x, y) (5)

(x cos "0 + y sin"0 , !x sin "0 + y cos "0) (6)

[Rz("0)!](x, y) = !(x cos "0 + y sin "0 , !x sin"0 + y cos "0) (7)

"0 "0 " 1 (8)

[Rz("0)!](x, y) # !(x, y) + "0

!y$!

$x! x

$!

$y

"(9)

Rz("0) # 1! i"0

hLz (10)

Lx, Ly, Lz (11)

:%'/')%&#)&E)&)'*;)$/6"#/,'%,1#5"#3\#H#

y

x

H!(r,") = #(r,") H!(r," + "0) = #(r," + "0) (1)

R("0)!(r,") = !(r," + "0) (2)

HR = RH (3)

"0 (4)

(x, y, z) (5)



"0 "0 " 1 (8)

[Rz("0)!](x, y, z) # !(x, y, z) + "0

!y$!

$x! x

$!

$y

"(9)

Rz("0) # 1! i"0

hLz (10)

Lx, Ly, Lz (11)

!L = !r ! !p (1)

!p =h

i!" (2)

"(x, y, z) (3)

H"(r,#) = $(r,#) H"(r,# + #0) = $(r,# + #0) (4)

R(#0)"(r,#) = "(r,# + #0) (5)

HR = RH (6)

#0 (7)

(x, y, z) (8)


(x!, y!, z!) (10)


#0 #0 $ 1 (12)

[Rz(#0)"](x, y, z) % "(x, y, z) + #0

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%y

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Rz(#0) % 1# i#0

hLz (14)

Lx, Ly, Lz (15)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (16)

{H, Lx} {H, Ly} {H, Lz} (17)

{H, Lx, Ly, Lz} (18)

V#6>%151"#2#"&##! !

x! ! x + !y

y! ! "!x + y

z! = z

!! 1

[Rz,!!] (x, y, z) ! !(x + "y , ""x + y , z)

! !(x, y, z) + "

!y#!

#x" x

#!

#y

"

Rz,! ! 1" i!

! Lz

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H!(r,") = #(r,") H!(r," + "0) = #(r," + "0) (1)

R("0)!(r,") = !(r," + "0) (2)

HR = RH (3)

"0 (4)

(x, y, z) (5)



"0 "0 " 1 (8)

[Rz("0)!](x, y, z) # !(x, y, z) + "0

!y$!

$x! x

$!

$y

"(9)

Rz("0) # 1! i"0

hLz (10)

Lx, Ly, Lz (11)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (12)

G&#0",'#5%&(#(."1(."1#,&"#</;"#01%01"#(%$$,&"##

H!(r,") = #(r,") H!(r," + "0) = #(r," + "0) (1)

R("0)!(r,") = !(r," + "0) (2)

HR = RH (3)

"0 (4)

(x, y, z) (5)



"0 "0 " 1 (8)

[Rz("0)!](x, y, z) # !(x, y, z) + "0

!y$!

$x! x

$!

$y

"(9)

Rz("0) # 1! i"0

hLz (10)

Lx, Ly, Lz (11)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (12)

{H, Lx} {H, Ly} {H, Lz} (13)

H!(r,") = #(r,") H!(r," + "0) = #(r," + "0) (1)

R("0)!(r,") = !(r," + "0) (2)

HR = RH (3)

"0 (4)

(x, y, z) (5)



"0 "0 " 1 (8)

[Rz("0)!](x, y, z) # !(x, y, z) + "0

!y$!

$x! x

$!

$y

"(9)

Rz("0) # 1! i"0

hLz (10)

Lx, Ly, Lz (11)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (12)

{H, Lx} {H, Ly} {H, Lz} (13)

H!(r,") = #(r,") H!(r," + "0) = #(r," + "0) (1)

R("0)!(r,") = !(r," + "0) (2)

HR = RH (3)

"0 (4)

(x, y, z) (5)



"0 "0 " 1 (8)

[Rz("0)!](x, y, z) # !(x, y, z) + "0

!y$!

$x! x

$!

$y

"(9)

Rz("0) # 1! i"0

hLz (10)

Lx, Ly, Lz (11)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (12)

{H, Lx} {H, Ly} {H, Lz} (13)

4",']%&#(."1(."1#,&"#</;"#01%01"#(%$$,&"#/,A#_#%0*1/'",1;###########################7##

H!(r,") = #(r,") H!(r," + "0) = #(r," + "0) (1)

R("0)!(r,") = !(r," + "0) (2)

HR = RH (3)

"0 (4)

(x, y, z) (5)



"0 "0 " 1 (8)

[Rz("0)!](x, y, z) # !(x, y, z) + "0

!y$!

$x! x

$!

$y

"(9)

Rz("0) # 1! i"0

hLz (10)

Lx, Ly, Lz (11)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (12)

{H, Lx} {H, Ly} {H, Lz} (13)

{H, Lx, Ly, Lz} (14)

-"6/#;"1/)'#'1%0#;)$06"#F#######################&"#(%$$,'"&'#0/;#"&'1"#",AK#

H!(r,") = #(r,") H!(r," + "0) = #(r," + "0) (1)

R("0)!(r,") = !(r," + "0) (2)

HR = RH (3)

"0 (4)

(x, y, z) (5)



"0 "0 " 1 (8)

[Rz("0)!](x, y, z) # !(x, y, z) + "0

!y$!

$x! x

$!

$y

"(9)

Rz("0) # 1! i"0

hLz (10)

Lx, Ly, Lz (11)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (12)

{H, Lx} {H, Ly} {H, Lz} (13)

{H, Lx, Ly, Lz} (14)

! # (15)

!L = !r ! !p (1)

!p =h

i!" (2)

"(x, y, z) (3)

H"(r,#) = $(r,#) H"(r,# + #0) = $(r,# + #0) (4)

R(#0)"(r,#) = "(r,# + #0) (5)

HR = RH (6)

#0 (7)

(x, y, z) (8)



#0 #0 $ 1 (11)

[Rz(#0)"](x, y, z) % "(x, y, z) + #0

!y%"

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Rz(#0) % 1# i#0

hLz (13)

Lx, Ly, Lz (14)

[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (15)

{H, Lx} {H, Ly} {H, Lz} (16)

{H, Lx, Ly, Lz} (17)

" $ (18)

[Lx, Ly] = ihLz (19)

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[&#,')6);/&'#6";#5*E)&)')%&;#


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Ly =h

i

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%&#$%&'1"#+,"#H##

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[Ly, Lz] = ihLx (20)

[Lz, Lx] = ihLy (21)

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Ly =h

i

!z

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!

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i

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Ly =h

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Lz!("r) = # !("r) (1)

d1 d2 M1 M2 (2)

I = M1d21 + M2d

22 (3)

$ = 0 $ = 1 $ = 2 (4)

LzY0,0(%,&) = 0 L+Y0,0(%,&) = 0 (5)

! !

0sin % d%

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0d& |Y",m(%,&)|2 = 1 (6)

H R(&0) = R(&0) H (7)

R(&0) (8)

= R(&0) '(r,&) = R(&0)"H !(r,&)

#= H

"R(&0)!(r,&)

#(9)

H (10)

'(r,& + &0) = H!(r,& + &0) (11)

'(r,&) = H!(r,&) (12)

H!(r,&) = '(r,&) H!(r,& + &0) = '(r,& + &0) (13)

! ' (14)

Lx, Ly (15)

&0 ! 1 (16)

[Rz(&0)!](x, y, z) " !(x + &0y , #&0x + y , z) (17)

y! " #&0x + y (18)

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$ # (9)

Lx, Ly (10)

"0 ! 1 (11)

[Rz("0)$](x, y, z) " $(x + "0y , #"0x + y , z) (12)

y! " #"0x + y (13)

x! " x + "0y (14)

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#= H

"R("0) $(r,")

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H (6)

#(r," + "0) = H$(r," + "0) (7)

#(r,") = H$(r,") (8)

H$(r,") = #(r,") H$(r," + "0) = #(r," + "0) (9)

$ # (10)

Lx, Ly (11)

"0 ! 1 (12)

[Rz("0)$](x, y, z) " $(x + "0y , #"0x + y , z) (13)

y! " #"0x + y (14)

x! " x + "0y (15)

%L = %r $ %p (16)

%p =h

i%% (17)

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0sin ! d!

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#= H

"R("0) $(r,")

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H (6)

#(r," + "0) = H$(r," + "0) (7)

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$ # (10)

Lx, Ly (11)

"0 ! 1 (12)

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y! " #"0x + y (14)

x! " x + "0y (15)

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! !

0sin " d"

! 2!

0d# |Y",m(",#)|2 = 1 (5)

H R(#0) = R(#0) H (6)

R(#0) (7)

= R(#0) $(r,#) = R(#0)"H %(r,#)

#= H

"R(#0)%(r,#)

#(8)

H (9)

$(r,# + #0) = H%(r,# + #0) (10)

$(r,#) = H%(r,#) (11)

H%(r,#) = $(r,#) H%(r,# + #0) = $(r,# + #0) (12)

% $ (13)

Lx, Ly (14)

#0 ! 1 (15)

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# (28)

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2I(29)

i#

I = M1d21 + M2d

22 (1)

! = 0 ! = 1 ! = 2 (2)

LzY0,0(",#) = 0 L+Y0,0(",#) = 0 (3)

! !

0sin " d"

! 2!

0d# |Y",m(",#)|2 = 1 (4)

H R(#0) = R(#0) H (5)

R(#0) (6)

= R(#0) $(r,#) = R(#0)"H %(r,#)

#= H

"R(#0) %(r,#)

#(7)

H (8)

$(r,# + #0) = H%(r,# + #0) (9)

$(r,#) = H%(r,#) (10)

H%(r,#) = $(r,#) H%(r,# + #0) = $(r,# + #0) (11)

% $ (12)

Lx, Ly (13)

#0 ! 1 (14)

[Rz(#0)%](x, y, z) " %(x + #0y , ##0x + y , z) (15)

y! " ##0x + y (16)

x! " x + #0y (17)

&L = &r $ &p (18)

d1 d2 (1)

I = M1d21 + M2d

22 (2)

! = 0 ! = 1 ! = 2 (3)

LzY0,0(",#) = 0 L+Y0,0(", #) = 0 (4)

! !

0sin " d"

! 2!

0d# |Y",m(",#)|2 = 1 (5)

H R(#0) = R(#0) H (6)

R(#0) (7)

= R(#0) $(r,#) = R(#0)"H %(r,#)

#= H

"R(#0) %(r,#)

#(8)

H (9)

$(r,# + #0) = H%(r,# + #0) (10)

$(r,#) = H%(r,#) (11)

H%(r,#) = $(r,#) H%(r,# + #0) = $(r,# + #0) (12)

% $ (13)

Lx, Ly (14)

#0 ! 1 (15)

[Rz(#0)%](x, y, z) " %(x + #0y , ##0x + y , z) (16)

y! " ##0x + y (17)

x! " x + #0y (18)

d1 d2 (1)

I = M1d21 + M2d

22 (2)

! = 0 ! = 1 ! = 2 (3)

LzY0,0(",#) = 0 L+Y0,0(", #) = 0 (4)

! !

0sin " d"

! 2!

0d# |Y",m(",#)|2 = 1 (5)

H R(#0) = R(#0) H (6)

R(#0) (7)

= R(#0) $(r,#) = R(#0)"H %(r,#)

#= H

"R(#0) %(r,#)

#(8)

H (9)

$(r,# + #0) = H%(r,# + #0) (10)

$(r,#) = H%(r,#) (11)

H%(r,#) = $(r,#) H%(r,# + #0) = $(r,# + #0) (12)

% $ (13)

Lx, Ly (14)

#0 ! 1 (15)

[Rz(#0)%](x, y, z) " %(x + #0y , ##0x + y , z) (16)

y! " ##0x + y (17)

x! " x + #0y (18)

d1 d2 M1 M2 (1)

I = M1d21 + M2d

22 (2)

! = 0 ! = 1 ! = 2 (3)

LzY0,0(",#) = 0 L+Y0,0(",#) = 0 (4)

! !

0sin " d"

! 2!

0d# |Y",m(",#)|2 = 1 (5)

H R(#0) = R(#0) H (6)

R(#0) (7)

= R(#0) $(r,#) = R(#0)"H %(r,#)

#= H

"R(#0)%(r,#)

#(8)

H (9)

$(r,# + #0) = H%(r,# + #0) (10)

$(r,#) = H%(r,#) (11)

H%(r,#) = $(r,#) H%(r,# + #0) = $(r,# + #0) (12)

% $ (13)

Lx, Ly (14)

#0 ! 1 (15)

[Rz(#0)%](x, y, z) " %(x + #0y , ##0x + y , z) (16)

y! " ##0x + y (17)

x! " x + #0y (18)

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! = 0 ! = 1 ! = 2 (1)

LzY0,0(",#) = 0 L+Y0,0(", #) = 0 (2)

! !

0sin " d"

! 2!

0d# |Y",m(",#)|2 = 1 (3)

H R(#0) = R(#0) H (4)

R(#0) (5)

= R(#0) $(r,#) = R(#0)"H %(r,#)

#= H

"R(#0) %(r,#)

#(6)

H (7)

$(r,# + #0) = H%(r,# + #0) (8)

$(r,#) = H%(r,#) (9)

H%(r,#) = $(r,#) H%(r,# + #0) = $(r,# + #0) (10)

% $ (11)

Lx, Ly (12)

#0 ! 1 (13)

[Rz(#0)%](x, y, z) " %(x + #0y , ##0x + y , z) (14)

y! " ##0x + y (15)

x! " x + #0y (16)

&L = &r $ &p (17)

&p =h

i&% (18)

! = 0 ! = 1 ! = 2 (1)

LzY0,0(",#) = 0 L+Y0,0(", #) = 0 (2)

! !

0sin " d"

! 2!

0d# |Y",m(",#)|2 = 1 (3)

H R(#0) = R(#0) H (4)

R(#0) (5)

= R(#0) $(r,#) = R(#0)"H %(r,#)

#= H

"R(#0) %(r,#)

#(6)

H (7)

$(r,# + #0) = H%(r,# + #0) (8)

$(r,#) = H%(r,#) (9)

H%(r,#) = $(r,#) H%(r,# + #0) = $(r,# + #0) (10)

% $ (11)

Lx, Ly (12)

#0 ! 1 (13)

[Rz(#0)%](x, y, z) " %(x + #0y , ##0x + y , z) (14)

y! " ##0x + y (15)

x! " x + #0y (16)

&L = &r $ &p (17)

&p =h

i&% (18)

! = 0 ! = 1 ! = 2 (1)

LzY0,0(",#) = 0 L+Y0,0(", #) = 0 (2)

! !

0sin " d"

! 2!

0d# |Y",m(",#)|2 = 1 (3)

H R(#0) = R(#0) H (4)

R(#0) (5)

= R(#0) $(r,#) = R(#0)"H %(r,#)

#= H

"R(#0) %(r,#)

#(6)

H (7)

$(r,# + #0) = H%(r,# + #0) (8)

$(r,#) = H%(r,#) (9)

H%(r,#) = $(r,#) H%(r,# + #0) = $(r,# + #0) (10)

% $ (11)

Lx, Ly (12)

#0 ! 1 (13)

[Rz(#0)%](x, y, z) " %(x + #0y , ##0x + y , z) (14)

y! " ##0x + y (15)

x! " x + #0y (16)

&L = &r $ &p (17)

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# (28)

E! =h2#(# + 1)

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I =12MR2 (26)

H =L2

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# (28)

E! =h2#(# + 1)

2I(29)

E! ! E!!1 # # (30)

R = 13 A (31)

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