iTunes library on external hard rive, move from macbook to macbook

I am sorry, I should have said in my explanation that iTunes on the new computer does not recognize the music folder I have in the external drive as a proper iTunes media folder. In other words, I had already tried the "option-Open" iTunes and I had chosen the external drive media folder but iTunes did not accept that as a proper media folder. Yesterday night, I made sure that the old/previous MacBook Pro did access the external drive as the Media folder, which it did. I also updated some iPhone/iPad apps and the files mentioned in various articles in the communities which are related to how iTunes stores its information (user/username/music/iTunes/ with endingings ".itl" and ".xml") were all updated, as well as the Media folder (on the external drive) where the apps are stored. So, iTunes on the previous/old computer perfectly accesses the actual music, apps, podcasts, etc... files on the Media folder in the external hard drive, while the iTunes music folder in the username address is properly updated. The version of iTunes in the old computer is the same as that in the new computer (I wrote 10.6, but it really is 10.6.3). The only other solution I have not tried is to copy the old computer iTunes folder (in the username address) and paste it in the proper location of the new computer, then choose the "option-Open" iTunes solution and try to choose the external hard drive Media folder. But, as I said in my original question, I am hesitant to do that because I don't want to loose all of my organized playlists if I make a mistake. Thanks again for your help.

thank you very much to everybody for the help.

It works..., by following Michael Allbritton suggestions as well as learning about iTunes organization from turingtest2.