There are situations which require one to recite two Amida prayers, one after another.
For instance, if a woman is praying Shacharit at home and she wishes to pray Mussaf immediately thereafter on Shabbat or Rosh Chodesh, however, she does not have enough time to recite the appropriate prayers and verses between the two Amida prayers and she wishes to only recite the Shacharit Amida prayer immediately followed by the Mussaf Amida prayer.
Similarly, if one forgot to pray any given prayer, one must recite a compensatory Amida during the next prayer, as we have discussed in recent weeks. For instance, if one forgets to pray Shacharit and remembers only once the time for Shacharit has elapsed, one must compensate for Shacharit by reciting a second Amida prayer immediately after reciting the Mincha Amida prayer.
The Gemara (Berachot 30b) states that one should not recite two Amida prayers immediately following one another; rather, one should wait a little while between the two prayers. The Gemara explains that reason for this is so that one may be able to pray in a manner of supplication and in a relaxed state of mind. However, if one prays two Amida prayers back to back, it appears as if one is doing so only to fulfill one’s obligation and be done with it and not in the appropriate manner of concentration and supplication.
Maran Ha’Shulchan Aruch (Chapter 105) rules, as follows: “One who prays two prayers one after another should pause between them for the amount of time it takes to walk four Amot so that one’s mind is relaxed and one will be able to pray in a manner of supplication.”
The “amount of time it takes to walk four Amot” quoted by Maran Ha’Shulchan Aruch is calculated as approximately three seconds between the two Amida prayers.
The above law applies to both of the situations mentioned above as well as regarding a Chazzan who has just concluded his silent Amida in that he must pause for several seconds before beginning the repetition of the Amida so that he can be relaxed and focused.
Summary: One who recites two Amida prayers immediately after one another must pause for several seconds between the two prayers so that one may be in a relaxed state of mind before beginning the next prayer.