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Amitabha Buddha is the Buddha of the Western Land of Ultimate Bliss:
The King of All Dharmas is the one word “Amitabha.”
The five periods and the eight teachings are all contained within it.
One who single-mindedly remember and recites his name,
In samadhi will enter the Thus Come One’s place of quiescence.”
Amitabha Buddha is also known as “Amitayus,” “infinite life.”  “Amitabha” means “infinite light.”  He is the Buddha of the Western Land of Ultimate Bliss.  The three Pureland Sutras: The Larger Sutra on Amitabha, The Smaller Sutra on Amitabha, and the Contemplation (visualization) of Amitabha Buddha Sutra.
Countless eons ago, Bhikshu Dharma Treasury made 48 inconceivable vows before Lokesvaraja Buddha. He vowed that his Buddhaland will be the most blissful and pure; that all who are born there will advance irreversibly to Buddhahood.  Bhikshu Dharma Treasury is now Amitabha Buddha.
A talk given by the Venerable Master Hsuan Hua:

“Speak one sentence more, recite the Buddha’s name one time less.  This is correct.  Speak one sentence less; recite the Buddha’s name one time more.  This is also correct.  If we understand this theory, then “when walking we recite Amitabha and when sitting we recite Amitabha.”  That is, when we’re walking, we recite Amitabha; when we’re sitting down we also recite Amitabha; when we’re standing we recite Amitabha, and even when we’re lying down, we recite Amitabha.  We recite constantly without the thought of reciting, and without the thought of reciting and yet reciting to the point that the wind cannot blow through and the rain cannot leak through; rather there is only the thought of reciting the Buddha’s name and nothing else.

Therefore it is said, recite the Buddha’s name continuously, reciting without a break.  The mouth recites Amitabha and makes things of a piece.  This happens when one’s recitations continue one after another, without stopping.  When extraneous thoughts do not arise, one attains samadhi.  If you don’t give rise to false thoughts, there is mindfulness, or proper perception.  That is *samadhi.”

Samadhi: “a state of deep meditative contemplation which leads to higher consciousness.”