自分が過去に実行したPBSジョブの情報を見ることはできるでしょうか？

はい、できます。
最初の方法は tracejob コマンドです。
以下は過去30日分のPBSログファイルを対象としてジョブを検索する作業例です。

m000% tracejob -n 30 11999
    
  Job: 11999.m000
    
  11/22/2005 10:36:53  S    Job Queued at request of userm000[dot]cfca[dot]nao[dot]ac[dot]jp,
                            owner = userm000[dot]cfca[dot]nao[dot]ac[dot]jp, job name = test.sh,
                            queue = short
  11/22/2005 10:36:53  S    Job Modified at request of
                            Schedulerm000[dot]cfca[dot]nao[dot]ac[dot]jp
  11/22/2005 10:36:53  S    enqueuing into short, state 1 hop 1
  11/22/2005 10:36:53  A    queue=short
  11/22/2005 13:26:53  L    Server job limit reached
  11/22/2005 13:35:27  L    Considering job to run
  11/22/2005 13:35:27  S    Job Modified at request of
                            Schedulerm000[dot]cfca[dot]nao[dot]ac[dot]jp
  11/22/2005 13:35:27  S    Job Run at request of Schedulerm000[dot]cfca[dot]nao[dot]ac[dot]jp
                            on hosts m004
  11/22/2005 13:35:28  L    Job run
  11/22/2005 13:35:28  A    user=user group=naocc jobname=test.sh queue=short
                            ctime=1132623413 qtime=1132623413 etime=1132623413
                            start=1132634128 exec_host=m004/0
                            Resource_List.cput=00:30:00 Resource_List.ncpus=1
                            Resource_List.neednodes=1 Resource_List.nodect=1
                            Resource_List.nodes=1
  11/22/2005 13:39:28  S    Obit received
  11/22/2005 13:39:28  S    Exit_status=0 resources_used.cpupercent=8
                            resources_used.cput=00:00:28 resources_used.mem=4324kb
                            resources_used.ncpus=1 resources_used.vmem=21992kb
                            resources_used.walltime=00:03:59
  11/22/2005 13:39:28  A    user=user group=naocc jobname=test.sh queue=short
                            ctime=1132623413 qtime=1132623413 etime=1132623413
                            start=1132634128 exec_host=m004/0
                            Resource_List.cput=00:30:00 Resource_List.ncpus=1
                            Resource_List.neednodes=1 Resource_List.nodect=1
                            Resource_List.nodes=1 session=24075 end=1132634368
                            Exit_status=0 resources_used.cpupercent=8
                            resources_used.cput=00:00:28 resources_used.mem=4324kb
                            resources_used.ncpus=1 resources_used.vmem=21992kb
                            resources_used.walltime=00:03:59
  11/22/2005 13:45:44  S    dequeuing from short, state 5

もしも過去30日以内のログファイルに当該ジョブの情報が見付からなければ、以下のように言われるでしょう。

m000% tracejob -n 30 478369
tracejob: Couldn't find Job Id 478369.m000 in logs of past 30 days

次の方法はコマンド qstat -fx です。
以下が例となります。

m000% qstat -fx 478369
Job Id: 478369.m000
    Job_Name = t2_Dec24
    Job_Owner = itootk@m000
    resources_used.cpupercent = 98
    resources_used.cput = 1358:01:11
    resources_used.mem = 6144kb
    resources_used.ncpus = 1
    resources_used.vmem = 458480kb
    resources_used.walltime = 1364:51:03
    job_state = R
    queue = long
    server = m000
    Checkpoint = u
    ctime = Mon Apr  7 17:13:34 2025
    Error_Path = m000:/home/itootk/Log.err
    exec_host = e122/0
    exec_vnode = (e122:ncpus=1)
    Hold_Types = n
    Join_Path = n
    Keep_Files = n
    Mail_Points = ae
    Mail_Users = itootkcfca[dot]nao[dot]ac[dot]jp
    mtime = Tue Jun  3 14:04:38 2025
    Output_Path = m000:/home/itootk/Log.out
    Priority = 0
    qtime = Mon Apr  7 17:13:34 2025
    Rerunable = False
    Resource_List.ncpus = 1
    Resource_List.nodect = 1
    Resource_List.nodes = 1
    Resource_List.place = scatter
    Resource_List.select = 1:ncpus=1
    stime = Mon Apr  7 17:13:34 2025
    session_id = 193397
    jobdir = /home/itootk
    substate = 42
    Variable_List = PBS_O_HOME=/home/itootk,PBS_O_LANG=en_US.UTF-8,
	PBS_O_LOGNAME=itootk,
	PBS_O_PATH=/home/itootk/bin:/opt/pbs/bin:/usr/local/bin:/usr/bin:/us
	r/local/sbin:/usr/sbin,PBS_O_MAIL=/var/spool/mail/itootk,
	PBS_O_SHELL=/bin/csh,PBS_O_WORKDIR=/home/itootk,
	PBS_O_SYSTEM=Linux,PBS_O_QUEUE=long,PBS_O_HOST=m000
    comment = Job run at Mon Apr 07 at 17:13 on (e122:ncpus=1)
    etime = Mon Apr  7 17:13:34 2025
    run_count = 1
    Submit_arguments = pbs_m000.sh
    project = _pbs_project_default
    Submit_Host = m000

(最終更新日 2025年6月3日)