Lec 3 - Symmetry and Group Theory

15
7/28/2019 Lec 3 - Symmetry and Group Theory http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 1/15         !"

Transcript of Lec 3 - Symmetry and Group Theory

Page 1: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 1/15

 

  

 

!"

Page 2: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 2/15

#

$$$$

$$

$%

$$

!

& #' #

( &

)% *+,- . * /.) (  

)% *+,- #

%

(

0$

Page 3: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 3/15

 

!

 " .1%2

.1 %*3+4

/$%.+!

5.6 %%

.6

%$5$/

$/$$. 6

%

$/

Page 4: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 4/15

$

$

%

#6

%

2#3

%7%8

9$#+

%

 

Page 5: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 5/15

# #

($

*

:

.

$

5

; 5

%

<$

' !

Page 6: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 6/15

($$$

($

5$

=----+>4

)92-?+44+-@)2> 

 $$

Page 7: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 7/15

(%

.+

.+ %$$)3

(%

.+ .+ %$$)3

(% .+

5$$)3

(% .+ 5$$)3

(% .+ %5$$A3

Page 8: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 8/15

3.A3

+.)3

1.4

3  %

+ %

1 0 ># 

! !

3B

!!;!'

+B .%

!$ ! !

#+ ≡ #3 ≡ σ

#

Page 9: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 9/15

1B/ %

0B$

>;

$!

*

3;+./ $

1'?$A3($4

0

;5@?1 $

;1

3./ ?

@ ?

?

;5@?1$

;1

3./ ?

@?

?

Page 10: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 10/15

;/ !

& +.1 1.+ / +#1 1/

C

& +.1 1.+ / +#1 1/

C 1

& +.1 1.+ / +#1 1/

C 1 4

& +.1 1.+ / +#1 1/

C 1 4 3& +.1 1.+ / +#1 1/

C 1 4 3

Page 11: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 11/15

& +.1 1.+ / +#1 1/

C 1 4 3 1& +.1 1.+ / +#1 1/

C 1 4 3 1 4

& +.1 1.+ / +#1 1/

C 1 4 3 1 4 3 D

 

D!

D!D E D E D

  !

!

$%%&%%%&$

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

Page 12: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 12/15

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 3×1×3

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 +×4×3

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1×3×3

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1

Page 13: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 13/15

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1 1

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1 1 4

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1 1 4 1

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1 1 4 1 3+ 3+-3+

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1 1 4 1 3+ 3

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1 1 4 1 3+ 3

Page 14: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 14/15

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1 1 4 1 3+ 3

+7 1 4 )1 1 4 )1 4 4

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1 1 4 1 3+ 3

+7 1 4 )1 1 4 )1 4 4

&7 6 4 4 6 4 4 3+ 3

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1 1 4 1 3+ 3

+7 1 4 )1 1 4 )1 4 4

&7 6 4 4 6 4 4 3+ 3

3 1 4 3 )1 4 )3 4 4

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1 1 4 1 3+ 3

+7 1 4 )1 1 4 )1 4 4

&7 6 4 4 6 4 4 3+ 3

3 1 4 3 )1 4 )3 4 4

+ 1 4 )1 )1 4 1 4 4

σσσσ σσσσ ΣΣΣΣ ΣΣΣΣ

Γ  1 4 3 1 4 3 D3+

37 1 4 1 1 4 1 3+ 3

+7 1 4 )1 1 4 )1 4 4

&7 6 4 4 6 4 4 3+ 3

3 1 4 3 )1 4 )3 4 4

+ 1 4 )1 )1 4 1 4 4

& 6 4 4 )6 4 4 4 4

C 3  A& 5

Page 15: Lec 3 - Symmetry and Group Theory

7/28/2019 Lec 3 - Symmetry and Group Theory

http://slidepdf.com/reader/full/lec-3-symmetry-and-group-theory 15/15

C 3  A& 5

  ' (

 )*&'

'

C 3  A& 5

 ! !     

(+*

"

C 3  A&  5

 '"!

!!!