New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

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

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Careers in Physics

by: Hayley Jenkins

Careers in Physics PHYS 690

Hayley Jenkins

GPA 3.66


Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Class Notes
25 ?




Popular in Course

Popular in Physics 2

This 1 page Class Notes was uploaded by Hayley Jenkins on Thursday October 29, 2015. The Class Notes belongs to PHYS 690 at College of William and Mary taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/231183/phys-690-college-of-william-and-mary in Physics 2 at College of William and Mary.


Reviews for Careers in Physics


Report this Material


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: 10/29/15
Notes Particle in a Box By Random Walks 7 Phys690 HW5 Spring 707 Shtwez39 Zhang The goal is to solve for the ground state of a particle in a box We set 7L m 1 The Hamiltonian is H 7 Vac where V is 0 when x is on 711 and 00 otherwise Note that this is the drunkard problem which we studied earlier in disguise As we have shown the solution to 8 7 at Iii16575 leads to the ground state of H at large t 11xt a 00 a 110 In the drunkard problem the probability distribution of the drunkard at large time is a smooth function which vanishes at the two bars According to the argument above this distribution is the ground state wave function of the quantum mechanical problem of a particle in a box Our strategy to solve the quantum mechanical problem is therefore to simulate the motion of many drunkards in order to obtain their distribution at large time Of course because of trapping at the bars there is a finite probability of losing the drunkard We would have to multiply 11xt by a constant to make up for that loss so as to ensure that the normalization of 11x t stays a constant ow we need to figure out how to simulate the drunkard motion The zeroth order description is that it is just diffusion Gaussian But boundary effect must be properly accounted for In the lattice version the drunkard either lands exactly at the bar or not In the continuum version however the situation is less straightforward there is always a nite probability that the drunkard will land at the bar and hence be absorbed Therefore we need to modify the Gaussian to take this effect into consideration Below is a more formal description We need to repeatedly operate exp7 rH on an initial wave function 739 is small Recall that exp7 rH E gxac is called the short time Green7s function It can be approximated by 1 90516 90xx 7 goIx if x amp ac inside box a otherwise where go is the free particle Green7s function 9015 1x 27W exp7x 722739 and 15 denotes the mirror image of ac with respect to the closer side of the box It is easily verified that 915 indeed satisfies 78987 Hg ii is 6 7 In at 739 0 and iii approximately satisfies the boundary condition at the sides Note that except for near the two sides 916 is essentially the free Green7s function 9015 K We want to propagate W15 CTEO g11acdx 2 The constant eTEO ensures normalization when 11 is the ground state wave function z39e when the propagation has reached equilibrium We can rewrite Eq 2 as we lama gem W cw lt3 1


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

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

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Amaris Trozzo George Washington University

"I made $350 in just two days after posting my first study guide."

Steve Martinelli UC Los Angeles

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

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund 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


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:

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

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.