At a time in its history when forces and factions are moving it apart, West Germany has been given a new chancellor, Helmut Kohl, with a reputation for harmonizing and moderating political differences, at least in his conservative Christian Democratic Union.

The question is: Can Kohl now soothe his nation, split increasingly across a broader spectrum of opinion?

That he comes from the right when the left in West Germany is resurgent has led to worries that his government will polarize the nation further. That he lacks the commanding personality of his predecessor, Helmut Schmidt, who was toppled Friday by a no-confidence vote in parliament, has fueled concerns that West Germany under him will lose its sense of things being held in place firmly and peaceably.

But Kohl's virtues -- his wholesomeness, decency and amiability -- while often ridiculed by hard-boiled Bonn journalists and politicians, play well with the middle class, where the new Bonn leader has said he intends to center his politics. His simplicity and forthrightness, even his verbal awkwardness, have a common-folk appeal and can be -- if exasperatingly unclassy at times -- also quite disarming.

Unfortunately for him, Kohl is off to an inauspicious start. A cloud of voter resentment and doubts hangs over the formation of his right-center coalition, which went about disposing of Schmidt through a parliamentary maneuver that dodged the public's preference, according to polls, for immediate national elections.

But speaking to reporters yesterday, Kohl seemed to have no second thoughts and showed unbounded enthusiasm for his new job.

His government is supposed to be a tentative one, coming to power under the promise -- although widely distrusted -- that national elections will be arranged early next year.

If the vote does happen, it could undo Kohl's government and complicate future coalition building by -- this is the scare scenario -- eliminating Kohl's junior coalition partner, the small, centrist Free Democratic Party, denying both major parties (Kohl's Christian Democrats and Schmidt's Social Democrats) an absolute majority and ushering into parliament the upstart, far-left Green Party. This is what happened in the state of Hesse last weekend and in Hamburg in June.

While appearing confident that he will remain chancellor for the long haul, Kohl indicated that he would be limiting policy initiatives for now to the domestic front. Foreign policy is Kohl's weakest field. He has limited international exposure and speaks no foreign language.

Kohl's top priority will be to deal with record unemployment -- approaching 2 million or about 7 percent of the work force -- and to revive an economy now in its third year of stagnation.

This is hardly a short-term objective. It depends as much or more on developments in the United States and on world trade conditions as on any new domestic policy program Kohl might put forward.

One advantage Kohl will have is a surge in West German business confidence that seems to have accompanied the conservatives' return to power. The financial and industrial community, depressed by the squabbling that characterized and ultimately paralyzed Schmidt's left-center government in the past 18 months, had hampered prospects of an economic turnaround by holding back investments. This is expected to change.

At the same time, what emerged from the revised budget program laid out this week by the new coalition was much less drastic than the Social Democrats' cries of "a return to primitive capitalism" would suggest. NEWS ANALYSIS

Some austerity measures were clearly things that Schmidt's party never would have tried, such as the cuts proposed in child allowances for large families. But for the most part, government under Kohl in the beginning is not apt to mark a sharp break with what it was under Schmidt. The most apparent difference probably will be in style.

In contrast to Schmidt, who is cool and highly disciplined in thought and emotion, Kohl is a hearty, affable, relaxed fellow.

His chubby face and large, (6 feet 4 inches) lumbering frame tend to reinforce the popular Bonn image of Kohl as a provincial character. But he has proven his staying power in politics against both Schmidt and the domineering Bavarian leader in his own bloc, Franz Josef Strauss, chairman of the Christian Social Union.

If there is a mystery to the new chancellor, it is the source of his seemingly unshakeable self-confidence. Aides and other politicians who have known Kohl for years continue to marvel at it.

Unlike Schmidt, who was versed in both military strategy and finance, Kohl has never developed an expertise in any special field. A senior aide said Kohl purposely avoided doing so because he regarded the image of generalist as more befitting a candidate for chancellor.

Kohl usually has been the youngest at whatever he has achieved--assemblyman in his home state of Rhineland-Palatinate at 29, leader of his party in the state parliament at 35, state premier at 39, national chairman of the Christian Democrats at 43, and now chancellor at 52.

For most of his working life, Kohl has been a professional politician, and aside from a few basic convictions -- he is a patriot, a Catholic, freedom-loving and strong on family and duty -- West Germany's new chancellor believes chiefly in himself.

Perhaps because of his abundant self-assurance, Kohl has a track record as a good team leader. As state premier, he attracted talented ministers and let them run on a long leash.

Since arriving in Bonn in 1976, Kohl has been somewhat less successful in securing loyalties and eliminating tensions among top party lieutenants. Still, his rivals all stopped short of challenging him openly in recent months for the chancellorship, and now they have fallen in behind him in the interest of party unity.

Sounding a bit like Ronald Reagan, Kohl struck a nostalgic cord yesterday, telling reporters he wanted to summon West Germans to "return to our strength" in reviving the economy. Such appeals may go down well with his own middle-aged generation. But the main riddle today of West German politics is how to win the confidence and adherence to traditional values of a younger generation drifting to the Greens.

Observers here will be watching closely to see whether Kohl's concept of politics by mediation can meet these challenges effectively. They also will be monitoring whether his talents of reconciliation can manage a Cabinet expected to be strained by bickering between his party's right-wing Bavarian allies and the free-market, centrist Free Democrats.