your trigger is very close;

inside a trigger, isntead of using @@identity, you wnat to use the virtual tables INSERTED (or DELETED, where approriate);

that virtual table allows oyu to handle multiple rows at teh same time, and already has teh new values generated from any identity() columns, calculated columns, etc.

USE [GroupTables]

GO

/****** Object: Trigger [dbo].[AddBarCode] Script Date: 07/15/2013 08:29:07 ******/

SET ANSI_NULLS ON

GO

SET QUOTED_IDENTIFIER ON

GO

-- =============================================

-- Author: <Tager, Kevin>

-- Create date: <7/13/2013>

-- Description:<Trigger to generate next barcode values on insert>

-- =============================================

CREATE TRIGGER [dbo].[AddBarCode]

ON [dbo].[StudentID]

AFTER INSERT

AS

BEGIN

-- SET NOCOUNT ON added to prevent extra result sets from

-- interfering with SELECT statements.

SET NOCOUNT ON;

-- Update the barcode numbers of the most recently Inserted Record

UPDATE [dbo].[StudentID]

SET [FoodBarcode] = [dbo].[StudentID].[AI] + 3289,

[LibraryBarcode] = [dbo].[StudentID].[AI] + 880101800707

FROM INSERTED --INSERTED and DELETED are virtual tables, inside a trigger, with the new/old values

WHERE [dbo].[StudentID].[AI]= INSERTED.[AI] --[AI] is the identity of the table/PK

END

GO