As you enter the student name call a javascript function to execute the ajax call then, Set the element that will receive the AJAX callback, like:

<div id="ajax-target">Ajax goes here!!!</div>

After that goto the custom code:

1--> Create a JavaScript function that will handle the call using jQuery.load(). The $nid in the path is just an example. It could be any variable.

<script>
        function myModule&#95;ajax&#95;load(name) {
          jQuery("#ajax-target").load("/node/ajax/"+name);
        }
    </script>

Note: please use _ in place of _ in above code

Write code in custom module:

2--> Register the URL that will render the HTML by implementing hook_menu():

    function myModule_menu() {
        $items['node/ajax/%'] = array(
            'page callback' => 'myModule_ajax_get_ajax', // Render HTML.
            'page arguments' => array(2),
            'type' => MENU_CALLBACK,
            'access arguments' => array('access content'),
            'delivery callback' => 'myModule_ajax_callback',  // Magic goes here.
        );
        return $items;
    }

3--> Create page callback and delivery callback functions:

function myModule_ajax_get_ajax($nid) {
        // You can return whatever you want, including forms.
        $node = node_load($nid);
        return node_view($node, 'teaser');
    }

    function myModule_ajax_callback($page_callback_result) {
        // Only render content
        $content = drupal_render($page_callback_result);

        // Add CSS and JS files, add some html
        $html = '' . drupal_get_css() . drupal_get_js() . '' . $content . '';
        print $html;

        // Perform end-of-request tasks.
        drupal_page_footer();
    }