(1) There are five requisites, the absence of which hinder the [proper] recital of a Service, even when its due time has arrived: ...Concentration of the mind.

(15) Concentration of the mind—how is this condition [to be fulfilled?] Any prayer uttered without mental concentration is not prayer. If a service has been recited without such concentration, it must be recited again devoutly. A person finds that his thoughts are confused and his mind is distracted: He may not pray till he has recovered his mental composure. (Hence, on returning from a journey or if one is weary or distressed, it is forbidden to pray till his mind is composed. The sages said that he should wait three days till he is rested and his mind is calm, and then he recites the prayers.)

(16) What is to be understood by concentration of the mind? The mind should be freed from all extraneous thoughts and the one who prays should realize that he is standing before the Divine Presence. (He should therefore sit awhile before beginning his prayers, so as to concentrate his mind, and then pray in gentle tones, beseechingly, and not regard the service as a burden which he is carrying and which he will cast off and proceed on his way. He should, accordingly, also sit awhile, after concluding the prayers, and then leave. The ancient saints were wont to pause and meditate one hour before the service, one hour after the service and take one hour in its recital.)

Rabbi Yoḥanan said: I saw Rabbi Yannai, who prayed and then prayed again. ... Later on, when this story was related in the study hall, Rabbi Yirmeya said to his teacher, Rabbi Zeira: What proof is there that the second prayer was the additional prayer? Perhaps initially he did not focus his mind on his prayer and ultimately he focused his mind, i.e., he repeated the morning prayer in order to do so with proper concentration.

(1) If one has recited the Amidah without devotion, he should recite it again devoutly. If he, however, concentrated his attention during the recital of the first blessing, he need not read the prayer again...