# Solution of the One-Speed Transport Eqn. by K M Case method

1. Jul 22, 2017

### Sharfu

1. The problem statement, all variables and given/known data
In the book, Nuclear Reactor Theory, Glasstone, Bell, under section 2.2
SOLUTION OF THE ONE-SPEED TRANSPORT EQUATION BY THE SEPARATION OF VARIABLES, I have difficulty in understanding the derivation. Hope some one can explain the derivation or give a reference where the derivation has been derived with explanation for the different (read each and every) steps. (The book is also available as TID 25606). The problem definition is equation 2.12. Then solved according to separation of variable methods for PDE.
2. Relevant equations
The ansatz solution thing is a new one (for someone with an engineering course in DE only) but mathematically viable. But why Mr. Case sought solutions with eigenvalues of Ψ? what is mathematical reason for it? As I am thinking the solution for "Source-Free Infinite Medium" as a sloped line going to zero as x increase toward infinity.
RHS of equation 2.14 contain an integral. Can someone show some link or reference where such PDE have been solved.
How integral of equation 2.19 is determined! What is the mathematical name for such calculation or some reference or link?
How can I see two discrete eigenvalues +vo and -vo satisfy equation 2.16?

3. The attempt at a solution
Spoiler: I admit I am a very slow learner, so do not get annoyed if I could not understand some very basic concepts. Secondly it would look too "demoralizing" if I skip a topic within first hundred pages of the book!

2. Jul 27, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.