Responsible party: poit0009, Hydra

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Please try to include the following

• main points understood, and expand them - what is your understanding of what the points were.
  • expand these points by including many of the details the class discussed.
• main points which are not clear. - describe what you have understood and what the remain questions surrounding the point(s).
  • Other classmates can step in and clarify the points, and expand them.
• How the main points fit with the big picture of QM. Or what is not clear about how today's points fit in in a big picture.
• wonderful tricks which were used in the lecture.
  

First, we start off with the question of why <math> < f_{p}|f_{p'}> =\delta (p-p^{'})</math> And what exactly does this mean?

To begin, we know that we can operate on an eigenfunction as follows: <math>\widehat{p}|f_{p}>=p|f_{p}></math> where we have simply multiplied “p” onto each part of the vector

So for any “Q” we have <math>\widehat{Q}|q_{n}>=q_{n}|q_{n}></math>

and we know that <math><q_{n}|q_{n}>=1 </math>

so for two vectors <math> q_{n} , q_{m} </math> we will have <math><q_{m}|q_{n}>=\delta _{m,n}</math>

So to solve the case for <math> f_{p}</math>, we know <math> f_{p}=Ae^{i\frac{p}{\hbar}x}</math> where the usual “k” has been replaced with <math>\frac{p}{\hbar}</math>

Then <math>\int_{-\infty}^{\infty}f_{p}^{*}\: f_{p^{'}}\; dx </math>

<math>= \int_{-\infty }^{\infty}e^{-i\frac{p}{\hbar}x}\: \; e^{i\frac{p}{\hbar}x}\; dx </math>

*This section posted in segments, so it's not complete yet*

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