HTML Calendar Input Form with jQuery

I want to use HTML text form input with calendar, and I found the way in this article.
That requires jQuery libraries links. Here is a procedure.

1. Adding following lines in HTML header section.

    <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
    <script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1/jquery-ui.min.js"></script>
    <script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1/i18n/jquery.ui.datepicker-ja.min.js"></script>
    <link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1/themes/redmond/jquery-ui.css" />
    <script>
    $(function() {
      $("#datepicker").datepicker();
    });
    </script>

1. Using following text box in the same html, we can use calendar input.

<input type="text" id="datepicker" name="StartDate" />

The most simple way is using a following input element, but it doesn't work in my HTML, maybe I declare XHTML 1.0. According to other sites, input type date is likely supported on HTML5.

<input type="date" name="StartDate" />

But I can use calendar input with jQuery even if the HTML is declared as XHTML 1.0.