How to overwrite behaviour of function in javascript

I am trying to override the behaviour of a javascript function for a website that I am developing. I am new to javascript and I am having a problem figuring this out. I have watched several videos and did some reading and this is what I came up with.

jQuery(document).ready(function ($) {

  function displayTab(element) {
    alert('here'); // test that I am getting here
    var tab = Drupal.quicktabs.tab
    // Set tab to active.
    $(this).parents('li').siblings().removeClass('active');
    $(this).parents('li').addClass('active');

    // Hide all tabpages.
    tab.container.children().addClass('quicktabs-hide');

    if (!tab.tabpage.hasClass("quicktabs-tabpage")) {
        tab = new Drupal.quicktabs.tab(element);
    }

    tab.tabpage.removeClass('quicktabs-hide');
    return false;
  }

  if ($( '#quicktabs-menu_block').length > 0) {
    $('#quicktabs-menu_block .quicktabs-tabs li').each(function() {
        $('a', this).bind({
            mouseenter: function(){
               $(this).displayTab($(this));
            }
        });
    });
  }
});

This is not working - the function is never called. I am not sure what that is, but obviously I am missing something fundamental. What am I missing?