How do I add jQuery Mobile.js?
There are jQuery Mobile module and Mobile jQuery Theme available. Looks like exactly what you wanted.


  The Mobile jQuery Theme is a powerful theme built on the jQuery Mobile platform. The theme adapts some of Drupal's base output to work with the highly themable designs built into the framework.


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  This is an enhancement module for the Mobile jQuery Theme. You can also hook into the module with you own theme if desired.


So you have the module to provide functionality you need, and theme you can use by creating subtheme, or as a reference.