jQuery Datepicker not open in jQuery Dialog after ajax call

Question

may you help me with a problem i tryed to solve this whole afternoon? I have a jQuery dialog, which i am filling up with the results (a php-script) of an ajax call. In these results there is a datepicker included, which will not open when i click on it. The datepicker is opening when i put it on a simple blank page.

Link clicked to open the dialog:

<a href="javascript: return false;" 
onclick="openGamePopup('.$this->gameID.')">Show details</a>    

The Ajax Function

function openGamePopup(gameID){
$('#standardDialog').dialog('option', 'title', 'Game Details');
  if (window.XMLHttpRequest){ // AJAX nutzen mit IE7+, Chrome, Firefox, Safari, Opera
        xmlhttp=new XMLHttpRequest();}
      else { // AJAX mit IE6, IE5
        xmlhttp=new ActiveXObject("Microsoft.XMLHTTP");}
  xmlhttp.onreadystatechange=function() {
    if (xmlhttp.readyState==4 && xmlhttp.status==200){
      document.getElementById("standardDialog").innerHTML=xmlhttp.responseText; 
    }
  }
  xmlhttp.open("GET","gameprofile.php?id="+gameID,true);
  xmlhttp.send();
  $("#gameTimePicker").css("z-index", "9999");
  $('#standardDialog').dialog('open');
}    

THe JQuery items

 $('#gameTimePicker' ).datetimepicker({
     changeMonth: true,
     changeYear: true,
     minDate: "+0d", 
     maxDate: "+90d",
     dateFormat: 'yy-mm-dd',
 });
$("#standardDialog" ).dialog({
    autoOpen: false,
    width: 600,
    height: 450,
  }
}); 

and last the PHP which fills the content of the dialog:

 if (isset($_GET['id'])) {$game= NEW Game($_GET['id']);}
 $game->showPopup();

 class Game{
 .....

    function showPopup(){ 

         echo ' <div style="font-size:11px;" align="center">
           <div><br/>Date and Time: 
           <input id="gameTimePicker" name="whenDate" type="date" /></div>';
         echo ' <div><br/>';
    }  
 }