"Understanding WKB Theory and Approximation

[nukestrom]

WKB theory?? Pls help

Homework Statement

WKB theory and WKB approximation. Are they same??

Homework Equations

I have to do a presentation about WKB theory in Physics (Quantum mechanics) but I don't know how to start from the WKB theory and come to WKB approximation. i.e. I don't find a direct connection. I know WKB theory is a method of solving differential equation but I do not know how to use it to solve any differential (well..2nd order) equation. It means I do not understand what WKB theory is (the basics) :( :(

The Attempt at a Solution

I tried to google and find the answer but did find a good explanation. I greatly appreciate if you can help me to understand this issue as this is vital to pass this course. Thanks.

 

[tiny-tim]

Welcome to PF!

WKB theory and WKB approximation. Are they same??
…
I tried to google and find the answer but did find a good explanation.

Hi nukestrom! Welcome to PF!

Googling is not a good phsycics research strategy.

Wikipedia is usually helpful, so best to start there … if you can't find anything on PF first, of course .

hmm … if you type "WKB theory" into wikipedia, you get the "http://en.wikipedia.org/wiki/WKB_theory" " page …

so I reckon they're the same!

 

[nukestrom]

Hi nukestrom! Welcome to PF!

Googling is not a good phsycics research strategy.

Wikipedia is usually helpful, so best to start there … if you can't find anything on PF first, of course .

hmm … if you type "WKB theory" into wikipedia, you get the "http://en.wikipedia.org/wiki/WKB_theory" " page …

so I reckon they're the same!

Thanks for your reply. I greatly appreciate it.

yes i did. I used wikipedia but their argument is not clear. They have proven it from few lines. As an example they have not explained "dominant balance" method which is essential to explain WKB. So wikipidea is good for expert but I want to learn basics.

 

[tiny-tim]

Have you tried googling for

"dominant balance" +WKB

(with the quotes marks)?

It should give you some google.books as well.

And searching this forum for "dominant balance" (again with quotes) gave 6 hits.

(I've never done WKB, so I'm afraid I can't help you any further.)

 

[Sjorris]

The WKB method is also sometimes called the W.K.B. method, or WKBJ, or even Liouville-Green. All I know is that it is an asymptotic technique used to determine large eigenvalues for oscillation solutions of differential equations. Maybe this extra information helps when googling for information.
Actually, I just looked it up in a PDE book by Haberman, and he refers to (after making implicit use of WKB) to Bender and Orszag (1999), Kevorkian and Cole (1996) and Nayfeh (2002), maybe your university library has these books.

 

[nukestrom]

Have you tried googling for

"dominant balance" +WKB

(with the quotes marks)?

It should give you some google.books as well.

And searching this forum for "dominant balance" (again with quotes) gave 6 hits.

(I've never done WKB, so I'm afraid I can't help you any further.)

Its Ok. Thanks anyway

 

[nukestrom]

The WKB method is also sometimes called the W.K.B. method, or WKBJ, or even Liouville-Green. All I know is that it is an asymptotic technique used to determine large eigenvalues for oscillation solutions of differential equations. Maybe this extra information helps when googling for information.
Actually, I just looked it up in a PDE book by Haberman, and he refers to (after making implicit use of WKB) to Bender and Orszag (1999), Kevorkian and Cole (1996) and Nayfeh (2002), maybe your university library has these books.

Thanks for your info. Yes, I use Orszag and got an idea about Dominant Balance method. But the transition (WKB theory) from the mathematical concept to quantum mechanical aspects is still not clear.
Thats the problem.

Thanks again for your info.