Hadith 1:

حَدَّثَنَا عَبْدُ الْوَاحِدِ بْنُ مُحَمَّدِ العبدوس [بْنِ عُبْدُوسٍ‌] الْعَطَّارُ رَضِيَ اللَّهُ عَنْهُ قَالَ حَدَّثَنَا عَلِيُّ بْنُ مُحَمَّدِ بْنِ قُتَيْبَةَ النَّيْسَابُورِيُّ قَالَ حَدَّثَنَا حَمْدَانُ بْنُ سُلَيْمَانَ قَالَ حَدَّثَنَا الصَّقْرُ بْنُ أَبِي دُلَفَ قَالَ سَمِعْتُ أَبَا جَعْفَرٍ مُحَمَّدَ بْنَ عَلِيٍّ الرِّضَا ع يَقُولُ‌ إِنَّ الْإِمَامَ بَعْدِي ابْنِي عَلِيٌّ أَمْرُهُ أَمْرِي وَ قَوْلُهُ قَوْلِي وَ طَاعَتُهُ طَاعَتِي وَ الْإِمَامُ بَعْدَهُ ابْنُهُ الْحَسَنُ أَمْرُهُ أَمْرُ أَبِيهِ وَ قَوْلُهُ قَوْلُ أَبِيهِ وَ طَاعَتُهُ طَاعَةُ أَبِيهِ ثُمَّ سَكَتَ فَقُلْتُ يَا ابْنَ رَسُولِ اللَّهِ فَمَنِ الْإِمَامُ بَعْدَ الْحَسَنِ فَبَكَى ع بُكَاءً شَدِيداً ثُمَّ قَالَ إِنَّ مِنْ بَعْدِ الْحَسَنِ ابْنَهُ الْقَائِمَ بِالْحَقِّ الْمُنْتَظَرَ فَقُلْتُ لَهُ يَا ابْنَ رَسُولِ اللَّهِ لِمَ سُمِّيَ الْقَائِمَ قَالَ لِأَنَّهُ يَقُومُ بَعْدَ مَوْتِ ذِكْرِهِ وَ ارْتِدَادِ أَكْثَرِ الْقَائِلِينَ بِإِمَامَتِهِ فَقُلْتُ لَهُ وَ لِمَ سُمِّيَ الْمُنْتَظَرَ قَالَ لِأَنَّ لَهُ غَيْبَةً يَكْثُرُ أَيَّامُهَا وَ يَطُولُ أَمَدُهَا فَيَنْتَظِرُ خُرُوجَهُ الْمُخْلِصُونَ وَ يُنْكِرُهُ الْمُرْتَابُونَ وَ يَسْتَهْزِئُ بِذِكْرِهِ الْجَاحِدُونَ وَ يَكْذِبُ فِيهَا الْوَقَّاتُونَ وَ يَهْلِكُ فِيهَا الْمُسْتَعْجِلُونَ وَ يَنْجُو فِيهَا الْمُسْلِمُونَ

Narrated that Abu Jafar Imam Muhammad bin Ali al-Rida (عليه السلام) said,

"The Imam after me is my son, Ali al-Naqi (عليه السلام). His command is My command, His word is My word, obedience to Him is obedience to Me. The Imam after him is his son al-Hasan al-Askari (عليه السلام). His command is His father’s command, His word is his father’s word, and obedience to Him is obedience to His Father."

Then the Imam became silent. 

I (the narrator) said, "O son of Allah’s Messenger, who is the Imam after al-Hasan Askari (عليه السلام)?"

The Imam (عليه السلام) cried a lot and then said, "After al-Hasan Askari (عليه السلام) is His son al-Qaim bil Haqq (the one who rises with truth), the Awaited."

I (the narrator) said, "O son of Allah’s Messenger, why is he called al-Qaim (عليه السلام)?"

The Imam (عليه السلام) said, "Because He will rise after the death of His remembrance and apostasy (murtad i.e., rejecting belief) of most of those who believe in His Imamate."

I (the narrator) said, "Why is he called the Awaited (Muntazar)?"

The Imam (عليه السلام) said, "Because He will have an occultation (ghaybah) of many days and very long duration. So the sincere/loyal ones will wait his rising and the doubters will reject Him and those who reject/deny will mock His remembrance (zekr) and those who will assign a time for his reappearance will lie, those who will hurry (be hasty regarding reappearance) in the period of Ghaybah will perish, and those who will submit in the period of Ghaybah will be saved."

[Source: Kamal al-Deen, Shaikh Sadooq, Ch. 36, Hadith. 3]

Hadith 2:

ورَوى محمدُ بن عجلان ، عن أَبي عبدالله (ع) قالَ : إِذا قامَ القائمُ (ع) دعَا الناسَ إِلى الإسلام جَديداً ، وهَداهُم إلى أمر قد دُثِرَ فَضَلَّ عنه الجمهورُ ، وانَّما سُمِّيَ الَقائمُ مَهدياً لأنَّه يَهْدي إِلى أَمرٍ قد ضَلُّوا عنه ، وسُمِّيَ بالقائمِ لقيامِه بالحقِّ

Narrated that Abu Abd-Allah Imam Sadiq (عليه السلام) said,

"When the Qaim (عليه السلام) rises, he will call the people to a renewed Islam, and wil guide them to a matter that has been forgotten and the majority have strayed away from. The Qaim (عليه السلام) is called the Mahdi because he guides to a matter that people have strayed away from, and he is called the Qaim because he will rise up with the truth."

 [(Source: al-Irshad, Shaikh Mufeed, Vol. 2, Pg. 383]