### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Atomic Physics PHYS 4261

GPA 3.67

### View Full Document

## 17

## 0

## Popular in Course

## Popular in Physics 2

This 0 page Class Notes was uploaded by Kylie Bartoletti DVM on Monday November 2, 2015. The Class Notes belongs to PHYS 4261 at Georgia Institute of Technology - Main Campus taught by Staff in Fall. Since its upload, it has received 17 views. For similar materials see /class/234287/phys-4261-georgia-institute-of-technology-main-campus in Physics 2 at Georgia Institute of Technology - Main Campus.

## Reviews for Atomic Physics

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 11/02/15

Physics 4261 Homework Set 2 Central Force Problem and Hydrogen Atom Friday January 25 2008 Please review Chapter 21 of Foot s book and the lecture notes 5 1 Prove that the kinetic energy of a 2 particle system is equal to the sum of kinetic energy associated with COM and relative motion ie 132 E Z m f A 2 where M is the total mass and u is the reduced mass N In the textbook the angular equation is solved using an algebraic method In this problem you will apply a direct approach to the differential equation below d z dF 1M 1 a m2 17 x2 Derive Equation 1 from the eigenvalue equation for the angular momentum operator LZY8 7121109 p Apply the parity operator to the equation What does this tell you about the solutions For the special case m0 this reduces to Legendre s equation Substitute FAF0 1 7 0 into this a power series solution F x 2L1ka and nd the appropriate k recursion relation between aHZ and ak aka P Show that gt k k 2 as k gt 00 What does this mean for the solution k at the poles 8 07 HINT Look at similar series Use this to nd the eigenvalue 7 The resulting solutions are the Legendre polynomials Px de ned for lxlg 1 D The Legendre polynomials may be written in the form P x Ld lkxz 71y 2 1 dx and the associated Legendre polynomials are P x 1 ixz39 Z Xm Px which satisfy Equation 1 above for m is Tabulate the Legendre polynomials 1 for 0I2 and 3 Verify that they are normalized t2 111310012 2m quot L n L 3X n ml ax a4 5amp1 L L m L 39 2quot La ling 3quot hurlquot 3 U L 1 SvHrcm k SL4 M x SMQ 74 WW5 ML MAAUL K 3 7539 U39 39 32 quotug Tu 5 139 2 h 7 1n gnu 2 M1 mm 3X x 3 MWLDX a 39L 1 Li 39 5 1 vm Ham 3X 3quot MN 23 x 7 1 Fl L a 2M 3 3 ht Quill 3X 7 MHzL W 2 4L 1 quotMM 31 f3939 i 5 Z 1 a A mmL 0X 39 y 3quot 2 A 2 2 gt a 142740124 70245 EQMWM ewk r 1392 2 Hbmf 422 BJ H 2 k A quotLucio A 1 2 J 3 l J 3 L 5 M w L 1 48 9 Ska 3839 933 941 9Jp 90 y Y I39m K 445 39 Shag 3 de a g 3 T W 0 4343 t sk 9 M sh 16 E9 T gm Mu W 9 my 4gt an m L a NM 3 E 1W N etim M mW m a w w m w A99 S g 3 SM3 33 39 6 65 swL kkk x use Tm 39 g 4mg so 5979 019 99 ale 9 4590 ampla Mar HAj Maw PM em m Tic AF Dlx li Fo B O Pad oftta u Them x L c an Po 046313 A Fx M w 3 2 if l x 35 3 PCquot 9 FOX is asL i m M wt SMQ H1 LAWN Marl l d fw 1 51kg P1 F m LL and eJuw 1ch Flag Pb Dr i4 Fx PM quot0 0453 Aon we 2ngFAFo F Equx 3 f EMU 0 c x Pea 45 2 3 K W XkZ QK hk lXHZ XRE 2 gathh h E uk all1 be M h AEQVx 0 L30 ILo n L1 so 2 akh Vt 0 X 2 maxVt AZP hut0 a 22 5 gmka gakxkbzh m i0 ya hUzh A kiln L1 kw Gui am chuuun 5 2 n knD 2k ward2 an a Qt qu gt an HBQQ thnfokhajr zzk LL an 931 MOO1 5 km SW 1044 Wt lowme Seam H x X1 H gt dud AW X211 LA emuv45 MAL To us unguk 3th at fie fbh n xt 9 off uc m wn ruva Kl lungm 39gt 0 pm 5M 11LAM TM A Um Mm Lang 1 l FECX E 145w ai akxk

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the material...plus I made $280 on my first study guide!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.