Oracle will convert your '11/23/2003' into a date, using what it thinks is a valid date format (see NLS for more info). On a UK NLS that might mean it is looking for dd/mm/yy, on a US system mm/dd/yy etc. How should it convert the century? Etc etc. It raises a lot of questions.
You should always remove any implicit date conversion by Oracle by forcing your value into a date.
Change you statement to....
and it will be guaranteed to work regardless of the current NLS settings (that assumes of course that SCH_DATE is a date column!).
select * from table1 where sch_date > to_date('11/23/2003','mm/dd/yyyy')
Please don't email me directly with questions. I've probably just got home from the pub and cannot guarantee the sanity of my answers. In fact, I can't believe I actually made it home.