The Federal Republic of Germany, born officially 30 years ago as the Western two-thirds of a divided and demolished country, celebrates its birthday Wednesday with its prosperity intact and its pride returning. Yet challenges ahead will test its self-confidence and still-young democracy in very different ways.

Those challenges form along three major lines: To find new goals, other than just more materialism and prosperity, for a new generation that was not traumatized by the Nazi era or the devastation that followed.

To develop more self-confidence in its democracy so that minor extremism does not produce overreaction.

To handle with care the emergence of West Germany as an incresingly important power, and not just in economic terms, in a world in which relationships have changed.

By any measure, West Germany's history of economic recovery and social stability has been, and remains, extraordinary.

Taking stock of the state of the nation before parliament last week, Chancellor Helmut Schmidt said, "Thirty years of the Federal Republic are not just 30 years of a state that functioned well or built itself up out of the ruins into one of the most economically productive countries of theworld.

Rather, it is also a state that has gained recognition and respect in thje world."

In effect, thje chancellor told the lawmakers that while the effort to overcome the Nazi past is not finished, the new state "now has a history of its own, that it is the best and most dignified part of German history," and that it already has existed longer than both the Weimer Republic of the 1920s, which broke down and give birth to the Hitler era, and the 12-year Nazi Third Reich.

Schmidt is right. Yet something is missing. The pride of the older generation today lies primarily in the economic recovery, which is perhaps understandable given the hunger and destruction of 1945. Yet a sense of national prupose beyond that is not quite there yet, especially for younger people.

"to us," says Stuttgart Mayor Manfred Rommel, 50, son to the famous World War ii field marshal, "progress was growth in the gross national product. Today's generation doesn't understand that at all, except to perhaps explain our generation's special experience right after the war.

"now they say they have much more different and human interests. Where is humanity, morale, self-fulfillment outside of profession, outside of material goods, they ask. Our problem is to find goals besides material progress and rebuild a general morale that can be trusted. We trust too much in law and too little in people."

Berlin Sen. Peter Glotz estimates that 10 to 20 percent of West Germany's university population feels isolated from society.

Schmidt himself, in many ways, symbolizes West Germany today.

At 60, Social Democrat Helmut Schmidt is the dominant and most respected political leader in West Europe, perhaps even in all the West.

Yet his pragmatic leadership and primary instincts lie overwhelmingly in the international monetary field. While he always comes down eventually on what liberals would call the "correct" side of touchy domestic and moral issues, he is acknowledged, even by his admirers, not to be out front on such issues and thus not especially inspirational to younger people.

It was schmidt's presence at the Guadeloupe summit meeting with the leaders of the United States, France and Britain in January that also symbolized both his increasing role as a world statesman and the fact that West Germany is no longer an economic giant anf political dwarf. Bonn plays an increasingly assertive role these days in NATO and the European Common Market.

And, no matter how strong the West German currency gets, the country continues to sell its products abroad, pile up enviable trade balances and thus continues to expand its international economic clout.

West Germany remains as steadfastly Western today as it was under Konrad Adenauer, who headed the country for its first 14 years.

West Germany is not likely to swap its allegiance and lifestyle for anything anybody else could offer. Yet new currents are stirring in big power relationships these days and it is impossible to say where they will lead.

Of primary importance is the continued relative growth of West German power, mostly economic, and the United States, the country that has protected and dominated Bonn's life for the past 30 years.

Combined with this is the fact that in another decade or so, the generation that grew up with the Marshall Plan, the Berlin airlift and a heavy diet of reliance of America will be out of power.

In addition, Bonn's policy of improved relations with its former enemies in the Communist Bloc remains of great importance here as a preserver of calm in Central Europe. The Soviet Union, to some extent, has also been courting Bonn, perhaps as a way to influence West German attitudes on alliance matters.

In sum, Bonn is emerging more as an international power at a time when old ideas are being tested and old faces disappearing. While there is no evidence of any fundamental West German shift, there are signs that Bonn is more intently seeking to protect its own interests and flanks against disruptions from either West or East.

At home, the balance sheet 30 years after the postwar constitution went into effect on May 23, 1949, is dominated by the statistics and a sense of material well-being that frequently overshadow social problems.

West Germany's 60 million people enjou one of the world's highest standards of living and most thorough social welfare systems covering health, education and retirement. West German production workers, averaging more than $9 an hour, are the best paid of any bog industrialized country.Correspondingly, West German labor costs to industry are now the world's highest.

Almost 35 percent of working men, but only 8 percent of working women, have incomes above $950 monthly.

In comparison to the United States, wealth seems more evenly distributed here, with relatively few obvious slum areas or very poor people. Unemployment, although steady at about 900,000, is a modest 3.8 percent.

Inflation, although shooting up to 8.5 percent for the first quarter due to a big jump in January, is expected to aremain about 3.5 to 4 percent for the year, the lowest for any major industrial power. Economic growth is forecast at 4 percent after adjustment for inflation.

Citizen action groups protesting nuclear power and high taxes have gwown here, belying somewhat the image of the obedient German. Yet there is not consumer movement to speak of.

On the darker side, the living conditions of the 2 million foreign workers who do the jobs Germans do not want, and the problem of integrating their 1 million children, remain a complicated blot on West German society.

Although terrorism here in the 1970s was minor in comparison to Italy, Spain or Northern iIreland, the West Germans reacted by enacting some very harsh laws that could come back to haunt them through miuse in another era.

In effect, West Germany's fledging democracy went through something of a mid-life crisis during the terrorist raids of recent years. It passed, but not with the highest marks.

Civil liberties remain restricted for extreme leftists in many conservative-ruled states. Authoritarianism remains the rule in most schools and continues to be a major source of streds in West german society.

Small bands of neo-Nazis have become bolder in recent years.

Yet a surge of new books, films and the airing of the American television series "Holocaust" have produced a generally healthy reaction, while educating youths on a subject that has been taboo in West German textbooks for the past 30 years.

"it was good that we were shocked by the Holocaust film," Chancellor Schmidt told the parliament last week.

"the young ones asked the older ones - was it really like this? And many of the older ones could onlynod their heads. The experience did not close the generation gap, but it opened a line of communication," he said. CAPTION: Picture, Chancellor Schmidt's state "now has a history of its own. It is the best and most dignified part of German history." Copyright (c) , Hennig Christoph