How to add an element right after the article using jQuery?

I think this is fine. But better do it like-

jQuery('div.entry-content').append('<div class="my-div"></div>');

Cause the $ sign doesn’t work some time with WordPress. Better if you wrap your jQuery code with this below code-

(function( $ ) {
    'use strict';

    // Write your jQuery code here.
    // And here you can use $ or jQuery as your wish.

})( jQuery );

Now about jQuery method, you can also use after() or insertAfter() to add something after the article tag.