- #1

Jimmy87

- 686

- 17

## Homework Statement

I am struggling with one of the end of chapter questions in my QM textbook (see attachment as I don't know how to show calculus on PF). It has thrown me because the chapter introduces some of the key principles in QM by talking about probability but then it randomly chucks in a question about the Gaussian distribution which is not covered at all in that chapter (or the whole book). Why have they put this question in there? What is the importance of this distribution to QM?

It asks you to solve for <x>. In the chapter it only briefly refers to <x> where it calls it an average and gives an example using some data. But what does it mean to take <x> (an average) of the Gaussian distribution?

I understand most of the integration but not the last bit. I don't get how there is a root pi over lambda in the final line at the end? If you look it up in the integral table it gives root pi over 2 lambda? Also in the table it says erf (u root lambda). Why does the solution not show this or do you ignore it? Also this integration in an integration of limits with respect to 'u' but how do you take the limits when the solution to the integral has no 'u' term in it?

## Homework Equations

see attachment

## The Attempt at a Solution

see attachment