Recent content by Kitty123

I am an undergrad with a husband and 4 kids. I work, tutor, work in a lab... all on top of my classes. I do really well on homework (and I really enjoy sitting and deriving with my white board) and I do well on our weekly quizzes. I stay above the average mark on everything... except exams; I...

Thinking about the Gaussian here as a probability makes sense (it also makes the second part of the problem much easier!) I will check out the link you sent after my kiddos go to bed! Thanks for all of your help!

A Gaussian was never explained to us as probability distribution. That makes this simpler. Thank you for your help.

The Gaussian was derived in a previous question. If the Yes. That was a typo. The full Gaussian has a (2^N)*sqrt(2/pi*N) in front of the exponential... so there is a factor of 1/sqrt(N). Am I correct in thinking that the multiplicity(all) in the probability should be the original Gaussian...

The Gaussian was derived in a previous question. If the distance traveled over N Assuming that x is the distance over N/2 steps I can say that x=r/2l where r is position, l is step length, and the factor of 2 comes from having to account for the absolute value of step length since I do not...

Ok... so now I need to use the Gaussian to write the probability of arriving at r. Probability is multiplicity(n)/multiplicity(all). I am assuming my Gaussian e^-r^2/2Nl (the Gaussian with x^2 replaced) is the numerator in my probability since this is the multiplicity function for arriving at r...

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OK. So if I am supposed to use a multiplicity like you said... but I am also supposed to map this onto a two state paramagnet which I solved in the previous problem... then I can use the factorial equation that I gave. In the state paramagnet that I solved I found that N-spin up = (N/2+x)...

Ok! That makes sense. The second part asks us to use the given Gaussian to calculate the probability, and I was assuming I needed to do that for part a... if I am just plugging things into a multiplicity function for part a that makes sense! Thank you.

I am suppose to express the variables from the random walk in terms of the variables for the paramagnet. I know that r= total distance traveled, delta= the change in placement, and R must be the total steps taken over N/2 since total steps over N/2* delta would give me a final distance traveled...

I understand the first part. A random walk is like a two state paramagnet because for every spin up or spin down you could go left or right. After looking back over my notes I think I plug-in delta^2/(2tau)*t for x^2... also in light of the second part of the question plugging this in for...

1. The question asks us to map a one dimensional random walk to a two state paramagnet and then write an expression for the number of journeys of N steps which end up at r=Rdelta. Then we are asked to find an expression for the probability that N steps will end up at r. 2...