Would Tim O'Brien be considered a writer of psychological realism writer in The Things They Carried?

"Realism" is a very broad but useful term that can be
applied to a wide range of literature. "Psychologica realism" should be, by definition,
a sub-category of "realism." I'll do my best to explain the two, very briefly, and to
answer your question about TIm O'Brien.

To begin with,
realism has nothing to do with "what actually happens." A perfect example of realism
could be completely fictional, for example, and there's even a very famous and popular
sub-category of realism called "magical realism," in which angels can fall from the sky
or butterflies can emerge from dying people's mouths. Instead, literary realism might be
defined as an attempt through literature to capture the lived experiences of people.
Realist authors pay very close attention to the environments of their characters as well
as to forces (e.g. economic class or racial or gender discrimination) that limit the
actions of individual charactesr in their works of
literature.

Henry James is often held up as one of the
primary examples of psychological realism. He is more concerned with his characters'
inner worlds, but he paints those worlds as convincingly as any realist author might. I
think that John Cheever's short story "The Swimmer" is a good example of psychological
realism. Cheever isn't concerned with telling a purely factual story, but he does paint
a convincing porrait of surburban America and the detrimental effects of excessive
alcohol use.

I'm less sure about Tim O'Brien's "The Things
They Carried." That story (and the collection with the same name) may fit in the
category of psychological realism, too. You may want to look at the narratory's
distinction in "Good Form" between "story truth" (a fictional but "true" treatment) and
"happening truth" (a factual but perhaps less "true" treament of the same
subject).