using wp login authentication for external php pages

Hi There

I am having a well working copy of wordpress website.
say http://www.abc.com/wp/ – wordpress path

I do have an external php application
say http://www.abc.com/apps/ – php application path

I wanted to know how to authenticate wordpress registered users to view the http://www.abc.com/apps page and that too it will display specific content of that user upon query using the username.

For example :
if user1 logins in wordpress from http://www.abc.com/wp he will be able to view http://www.abc.com/apps/
contents of user1 is displayed
or
if user2 logins in wordpress from http://www.abc.com/wp he will be able to view http://www.abc.com/apps/
contents of user2 is displayed

I have a mysql query already working fine in http://www.abc.com/apps like
“select * from tablename where username=$wp_username and password=$wp_password”

do i need to reauthenticate again with the username and password in apps file or is there any possibilities to use the wp session to display particular user content.

the purpose is i dont want 2 login forms for wordpress and apps as all the users are same in wordpress and apps

Kindly advice how to use wp login session to hook.