Notify post author once a new post is published

/** Notify post author once a new post is published **/

function notify_author($post_id) {

$post = get_post($post_id);
$author = get_userdata($post->post_author);
$subject = "A new Post Published: ".$post->post_title."";

$message = "
      Hi ".$author->display_name.",

      Your post, \"".$post->post_title."\" has just been published.

      View post: ".get_permalink( $post_id )."

      Thanks"
      ;

   wp_mail($author->user_email, $subject, $message);
}
add_action('publish_post', 'notify_author');