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## COMMUTATIVE ALGEBRA

by: Miss Thora Marquardt

23

0

1

# COMMUTATIVE ALGEBRA MATH 260

Miss Thora Marquardt
UCR
GPA 3.98

John Baez

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COURSE
PROF.
John Baez
TYPE
Class Notes
PAGES
1
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 1 page Class Notes was uploaded by Miss Thora Marquardt on Thursday October 29, 2015. The Class Notes belongs to MATH 260 at University of California Riverside taught by John Baez in Fall. Since its upload, it has received 23 views. For similar materials see /class/231733/math-260-university-of-california-riverside in Mathematics (M) at University of California Riverside.

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Date Created: 10/29/15
Math 260 Perturbation theory Miguel Carrion Alvarez 1 The perturbation series Starting With z z 2 I I I I 1W Hamiveeztwrn71gtHoWHOHOiVel 1Ho dt1dtn1 dtn n20 0 0 0 we get 1 1 2 MOPZA A A iiVe iquot quot1H e i 2quot1H iiVe i 1H 12dt1ndtwgdtw r n21 1 En t2 1 2 iiHo6 lquot quotH e lm hm iiVe quot1H z2dt1dtn1dtn 0 0 0 n21 iV HuhJO Which is Schrodingerls equation 2 The perturbation series in the interaction picture 1 tn 2 I I tZOO E ZO WWOiiVe Z quotquotquot 1H WWWHOiiVe quot1H 12dt1dtn1dtn n20 2 tn 2 eiitHo HI eitho fiVeiitho Illeit1Ho flVeiit1Ho1dt1 I I dtnil dtn 0 0 0 n20 implies ma g quotOt2iiwn avgowdtlnutwldtn 3 Ground state transition amplitude Using the facts that H01 07 and H02 z and the representation a N a and a N z lt1yeiizit1Ho fiVeiit1H01gt lt17eiititlHo a aeiit1H01gt lt17eiitit1Ho a a1gt i eii 1Ho0 Lu 64011 LeimitiNl Zgt 0 Similarly7 lt17eiititzHofiveiitzit1Hofiveiit1H01gt 7Tvlt17eiititgHo a aeiitgitlHo a a1gt 2 lt1yeititzHo a aei12711Ho 0 4 2 2 e lt2tllt1ye ltitzHo aazgt 4 2 2 eil 2tllt1yeil 2Ho 1 22 7A2 2 6711211lt171 671titz222gt 7A2 A2 4127 1 7 iQZ tl 2 e ltllgt 2 e

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