×

### Let's log you in.

or

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

×

or

## Careers in Physics

by: Hayley Jenkins

25

0

1

# Careers in Physics PHYS 690

Hayley Jenkins

GPA 3.66

Staff

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

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

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

×
Unlock Preview

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

## 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

×

×

### What is Karma?

#### 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

×

×

### BOOM! Enjoy Your Free Notes!

×

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

#### 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