I would argue that while the Vietnam triggered many different emotions within the American public, the one common ground of agreement is that the death of our soldiers is an extremely painful moment. Even the most staunch war advocates and war opponents can examine the Vietnam Memorial and feel a sense of awe in its presence. While political discourse can be heated and represent the essence of divergence, the Vietnam Memorial can be a point of convergence, for all can honor those who have made the ultimate sacrifice. In the most odd of ways, this becomes the only common ground on the war, itself. Few can deny that the war was the preeminent issue in the mid to late 1960s and beyond. To this day, arguments about the war's need could provoke fisticuffs. Yet, the Vietnam Memorial brings harmony to where disharmony might have reigned supreme.
I agree with pohnpei in that perhaps national unity is the wrong way to describe it. Unifying in that those who were for or against the war could nevertheless agree on the fact that the loss of 58,000 Americans was a tragedy, and that they should be honored for their sacrifice. Some have argued that it was a healing symbol by allowing both civilians and veterans to connect with those they lost in the war, and to leave offerings, poems, shrines, etc. in a final connection with them (a stunning exhibit of items left at the Wall is on permanent display at the Smithsonian Museum of American History in Washington DC).
The Vietnam War was a very painful chapter in American history and the Wall has allowed many Americans to begin, at least, to process and heal from that grief.
The Vietnam War (or "conflict," to be more precise) was one of the most divisive events in American history. It was a highly unpopular war, spurring thousands of protests around the country as well as the rest of the world. American soldiers who served there were also the brunt of unfair criticism for taking part in the "police action." The construction of the magnificent Vietnam Memorial in Washington, D. C. serves as a reminder of the 50,000+ American soldiers who gave their lives; each American soldier who died during the war has their name inscribed on the wall. It also serves a reconciliatory function for all people who lived during those times--with both pro- and anti-war beliefs--to now unite in honor of those who gave their lives.
If you have never seen the memorial, by all means do so if you ever visit the nation's capital. It is especially beautiful when seen at night.
I don't know that you can prove that it is... I wonder if your book says something specific about this that you are supposed to write down as an answer.
If I had to make this argument, I would say that the memorial is a symbol of national unity because it is meant to honor those who died in war. This is an attempt to make up for how badly the Vietnam veterans were treated by many people after they came back from the war. So it is an attempt to reach out to them and to acknowledge their sacrifices.
I don't see, however, how it would reach out to the people who hated the war -- I don't see how it brings them back to being united with the rest of the country.