12.01.2015 Views

UNIVERSIT . . AT BONN Physikalisches Institut - Universität Bonn

UNIVERSIT . . AT BONN Physikalisches Institut - Universität Bonn

UNIVERSIT . . AT BONN Physikalisches Institut - Universität Bonn

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

¾º¿ ËØÖÙÙÒ ×ÛÖ Ó×ÓÒÒ<br />

Ö Ò ÄÓÖÒØÞ×ÐÖ ×ظ ÐØ × ÊÐØÓÒ Ò ÐÐÒ ÞÙ××Ý×ØÑÒº Ö Ò<br />

ÌÐÒ¸ × × Ò z¹ÊØÙÒ Ûظ ÖØ × ÙÖ ÑØ p μ =(E,0, 0,p)<br />

ɛ μ (λ =+1) = − √ 1<br />

2<br />

(0, 1,i,0)<br />

ɛ μ (λ = −1) = √ 1<br />

2<br />

(0, 1, −i, 0)<br />

´¿µ<br />

Ö ØÖÒ×ÚÖ×ÐÒ ÃÓÑÔÓÒÒØÒ¸ Ö<br />

ɛ μ (λ =0) = 1 (p, 0, 0,E)<br />

m<br />

´¿µ<br />

Ö ÐÓÒØÙÒÐ ÃÓÑÔÓÒÒغ Ð×Ó Û×Ø Ö ÐÓÒØÙÒÐ W ¹Ó×ÓÒÒ ×Ö Î¹<br />

ÖÖÚØÓÖ ÐÒÖ ÑØ Ñ ÁÑÔÙÐ× Òº Ö ×Ö Ó ÒÖÒ ´E ≫ mµ ÓÐØ<br />

ɛ μ long.<br />

= 1 m pμ . ´¿µ<br />

ÍÖ× Ö × ×ÐØ ÀÓÒÖÚÖÐØÒ Ò Ö ËØÖÙÙÒ ×ÛÖ Ó×ÓÒÒ<br />

×Ò ×ÓÑØ ËÙÔÖÓÞ×× V L V L → V L V L º<br />

ÈÝ×Ð× ÒØÖ××ÒØ ×Ø ÒÙÒ Ö¸ ÛÐÖ ËÛÖÔÙÒØ×ÒÖ √ s ÍÒع<br />

ÖØØ ÚÖÐØÞØ ÛÖ¸ ÙÑ ÖÙ×ÞÙÒÒ¸ × ÛÒÒ ÎÓÖÖ×Ò Ö ËŹÌÓÖ ÒÓ ÐØ<br />

×Ò ÙÒ ÛÒÒ × ÞÙ×ÑÑÒÖÒ ÙÒ × ÆÙ ÈÝ× ÒØÛÖ ÖØ ÓÖ<br />

ÒÖØ ÑÖÖ ÑÒ ÑÙº<br />

Ù ÒÒ Ö ÀÖÐØÙÒ ÒÖ ×ÓÐÒ ÖÒÞ ÛÖ × ÐØÖÓ×Û ÕÙÚÐÒÞØÓ¹<br />

ÖÑ ½¿℄ Ù×ÒÙØÞØ ØÖØØ ÑÒ ËØÖÙÙÒÐÓÒØÙÒÐÖ ×ÛÖ Ó×ÓÒÒ¸<br />

V L V L → V L V L¸×ÓÐØ Ö s ≫ M V <br />

A(V 1 L V 2 L → V 1 L V 2 L ) = A(ω 1ω 2 → ω 1 ω 2 )+O( M 2 V<br />

s ) .<br />

×Ò ω i ÓÐ×ØÓÒ¹Ó×ÓÒÒ¸ Ò ÐÓÒØÙÒÐÒ ÃÓÑÔÓÒÒØÒ Ö Ó¹<br />

×ÓÒÒ V i ÒØ×ÔÖÒ ´Úк ×ÒØØ ¾º¾µº × ÙØظ ÒÖÒ s ≫ M V<br />

ÖÒÙÒÒ ÚÓÒ ÑÔÐØÙÒ Ò×ØØØ ÑØ ÖÐÒ ´ÚØÓÖÐÐÒµ Ó×ÓÒÒ Ù ÑØ<br />

Ò ÒØ×ÔÖÒÒ ´×ÐÖÒµ ÓÐ×ØÓÒ¹Ó×ÓÒÒ ÙÖ ÖØ ÛÖÒ ÒÒÒº<br />

ØÖØØ ÛÖ ÒÙÒ ÐÐÑÒ ÑÔÐØÙ Ö ÒÒ 2 → 2 ¹ËØÖÙÔÖÓÞ×× ×ÐÖÖ ´=<br />

×ÔÒÐÓ×Öµ ÌÐÒº × ÐØ<br />

dσ<br />

dΩ = 1<br />

64π 2 s ·|A|2 .<br />

´¼µ<br />

ÖÐØ ÑÒ ÑÔÐØÙ Ò ÒÞÐÒ ÈÖØÐÛÐÐÒ¸ ÔÖÓÔÓÖØÓÒÐ ÞÙ ÙÐ×ÝÑÑØÖ×Ò<br />

ÄÒÖ¹ÈÓÐÝÒÓÑÒ P l (cos θ)¸ ×Ó ÐØ × ×ÑØ ÑÔÐØÙ Ð× ËÙÔÖÔÓ×ØÓÒ ÙÒ¹<br />

ÒÐ ÚÐÖ ×ÓÐÖ ÒÞÐÛÐÐÒ ÑØ ÛÐ× ×ØÑ ÖÑÔÙÐ× l Ö×ØÐÐÒ<br />

A =16π<br />

´¿µ<br />

∞∑<br />

(2l +1)P l (cos θ) · a l , ´½µ<br />

l=0<br />

ÛÓ a l ËØÖÙÑÔÐØÙ Ö ÈÖØÐÛÐÐ ÑØ ÖÑÔÙÐ× l ×غ Ö ØÓØÐ ÏÖÙÒ×¹<br />

ÕÙÖ×ÒØØ σ ÖØ × ÑØ ÙÒØÖ Ù×ÒÙØÞÙÒ Ö ÇÖØÓÓÒÐØØ Ö ÄÖÒÖ¹<br />

ÈÓÐÝÒÓÑ ÞÙ<br />

σ = 16π ∞∑<br />

(2l +1)|a l | 2 . ´¾µ<br />

s<br />

l=0<br />

½¿

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!