Part of my approach to teaching is requiring students to write questions about lectures, articles, textbooks, and Biblical texts. (Trying to help them be more Socratic in their own approach to learning). One of my students asked the following question (with my reply following):
STUDENT: In regards to the Psalms and Proverbs I always believed and was taught that David wrote Psalms and Solomon wrote Proverbs. Is that still believed to be true from you Scholars or is there a cross over of Solomon also writing the end of Psalms?
When considering issues of authorship we begin with self-claims in the texts we are examining (rather than simply tradition passed down, which is not dismissed, but relegated to a lesser role in determining who wrote what).
In the case of the Psalms, there are many with the name of David attached to them (eg, 3, 4, 5, etc.). But some are attributed to others: one to Solomon (72), one to Moses (90), some to Asaph (eg, 50, 73, 74, etc.), some to “the sons of Korah” (eg, 42, 44, 45, etc.), etc. Many have no self claims (eg, 1, 2, etc.). Some of the notations saying “of XXX” may not actually be a claim of who authored, but simply who might be associated with the song (particularly with regard to the songs attached to David). Finally, someone comes along sometime (at the very earliest) in the Exile and compiles five scrolls (see the notes in your Bible at the headings of Psalm 1, 42, 73, 90, and 107) filled with songs from their history that they have selected to include (that we call the Book of Psalms). Very likely this particular grouping appears later than the Exile in the form it occurs in our versions. [As an aside, there are some manuscripts we have found which have differing claims attached to some of the psalms as well as being other psalms in other collections including the one pictured below that we have called Psalm 151 from cave 11 at Qumran]
With the Proverbs there are several places attributing several of the collections to Solomon (1:1 prefacing chapters 1-9; 10:1 prefacing chapters 10-24), one collection that is attributed to Solomon but collected by men in the days of Hezekiah (25:1 prefacing chapters 25-29), and then two collections at the end of the book that are by men we don’t know almost anything about beyond their names: Agur (30:1 prefacing chapter 30) and King Lemuel taught him by his mother (31:1 prefacing chapter 31). Finally someone (at the very earliest) would have complied these in the days of Hezekiah (or as seems very likely, much later) into the collections we have in our book.
Of course, what we have in these cases are attributions and/or claims of authorship which could still be questioned upon historical bases. But we still do well to at least begin with the self-claims of the texts themselves even if we later may note features indicating other hands/minds involved.