Which enterprise search engine does amazon use on amazon.com to search for items?

Answer 1

Amazon uses its own proprietary software to run its store, content management system, etc. They name different components of their software after parts of the Amazon river, like obidos (you see this in Amazon's URL).

They write their own software because their site is far too complex and specialized, and receives such high traffic volume that practically any third-party product would be inadequate.

Answer 2

Amazon.com does not use a search engine, they use Web Services to do all the searching.