declare @tablea table
(
	ssn 		int,
	applicationtime datetime
)

declare @tableb table
(
	ssn 		int,
	admissiontime 	datetime,
	dischargetime	datetime
)
insert into @tablea
select	1234, '1/1/2005'	union all
select	1234, '2/1/2006'	

insert into @tableb
select	1234, '1/9/2005', '1/23/2005'	union all
select	1234, '2/7/2006', '3/31/2006'

select	a.ssn, a.applicationtime, b.admissiontime, b.dischargetime
from	@tablea a inner join @tableb b
	on	a.ssn			= b.ssn
	and	a.applicationtime	<= b.admissiontime
	and	b.admissiontime	= (select top 1 y.admissiontime
						from	@tablea x inner join @tableb y
						on	x.ssn	= y.ssn
						and	x.applicationtime	= a.applicationtime
						and	x.applicationtime	<= y.admissiontime
						order by datediff(day, x.applicationtime, y.admissiontime)
					)

/* RESULT
ssn         applicationtime          admissiontime             dischargetime                                          
----------- ------------------------ ------------------------- -----------------------
1234        2005-01-01 00:00:00.000  2005-01-09 00:00:00.000   2005-01-23 00:00:00.000
1234        2006-02-01 00:00:00.000  2006-02-07 00:00:00.000   2006-03-31 00:00:00.000

(2 row(s) affected)
*/