If your landing page is your front page, in $variables, you have a key named is_front. You can use that to see if you are currently on the home page and add your JS if the value is true.
function bartik_preprocess_html(&$variables) {
if ($variables['is_front']) {
drupal_add_js(...);
}
}
If it's not your front page, you can set the theme_debug setting to TRUE in your settings.php to identify the name of a custom template file that you can use. Just duplicate page.tpl.php and add your custom js in the head or in the footer. Example of my front page when I use theme_debug (html commments) :
<!-- THEME DEBUG -->
<!-- CALL: theme('page') -->
<!-- FILE NAME SUGGESTIONS:
* page--front.tpl.php
* page--node--1.tpl.php
* page--node--%.tpl.php
* page--node.tpl.php
x page.tpl.php
-->
<!-- BEGIN OUTPUT from 'themes/bartik/templates/page.tpl.php' -->
I can clone page.tpl.php to page--node--1.tpl.php to have my specific JS included for that page only.