The Gemara in Masechet Shabbat (150) establishes the prohibition against speaking about one's business operations on Shabbat. This prohibition is derived from a verse in the Book of Yeshayahu (58:13), where the prophet speaks about refraining on Shabbat "Mi'metzo Cheftzecha Ve'daber Davar" ("from pursuing your needs and speaking of matters"), which is interpreted as referring to speaking of one's professional and commercial pursuits.
Accordingly, the Shulchan Aruch rules (306:8) that one may not speak of business-related matters on Shabbat. Thinking about such matters in one's mind, he adds, is, strictly speaking, permissible, though due to the obligation of Oneg Shabbat (enjoying oneself on Shabbat) it is a Mitzva to avoid even thinking about one's business on Shabbat. The Shulchan Aruch writes that on Shabbat one should feel as though all his work has been completed and he has no lingering or outstanding responsibilities that should concern him. The Torah instructs, "Six days shall you labor and perform all your work" (Shemot 20:9). As the Midrash notes, a person can never be said to have performed "all his work"; one always has more work that he can do. The Midrash explains that the Torah here demands that on Shabbat one look upon his work as having been completed, and he should therefore not even think about any of his professional responsibilities. Particularly, if thinking of one's business causes stress and anxiety, he must avoid thinking of such matters on Shabbat.
Summary: Halacha forbids speaking of business-related matters on Shabbat. Thinking about such matters is technically allowed, though it is a Mitzva to feel on Shabbat as though all his work is completed, especially if thinking of his business will cause him anxiety.
