The forlorn and familiar scene of teen-agers milling aimlessly in front of the unemployment offices in big American cities may disappear in the 1980s, a growing number of sociologists and population experts say.

The staggering national problem of teen-agers seeking jobs that are not there -- and the corollary problems of crime and social dislocation that flow from it -- are rooted in the sheer numbers of these young people, and those numbers are now heading into a longterm decline.

The children of the nation's "baby boom" of the 1940s and 1950s and early 1960s were the young adults standing in those unemployment lines. Now they are older. They will be succeeded by a much smaller group of young people, those born in the last 18 years, and this will relieve pressure on the job market and help ease a wide range of serious social problems.

Minorities have suffered most in the scramble for entry-level jobs. But white teen-agers were hurt, too. Their unemployment rate has been about 14 percent -- compared with 6 percent unemployment among all adults in the labor market.

Economists like Michel L. Wachter and Richard A. Easterlin of the University of Pennsylvania are predicting that during the 1980s and certainly by the 1990s there will be a "dramatic decline" in the unemployment rate.

And Easterlin is also predicting that there will be a "turnaround or amelioration in a wide variety of . . . social, economic and political conditions."

He says unemployment wil go down, crime rates will dip, there will be a slowdown in the burgeoning of divorce, and a decline in the alarming suicide rates among young males.

The philosopher's stone behind these happy changes is the decline in the fertility and birth rates in the United States in recent years.

Startling in the late 1950s, American families began having fewer children on the average, and now those babies are approaching maturity. There will be millions fewer of them.

The year 1980 will be the peak year for persons age 18 to 24, with 29.5 million. But by 1995, as a result of declining fertility in the last decade or so, the 18- to 24 age group will shrivel to 23.2 million. This is not just theory, because these children have already been born and it is known how many will be reaching late teens and young adulthood 10 to 15 years down the road.

As the 1980s and 1990s progress, this will produce a severe shrinkage in the number of teen-agers and young adults coming into the labor force, entering schools and the like.

Competition for jobs, for college entry, just general crowding in this age category will be reduced, and many of the unfavorable social conditions associated with the baby bulge of the past generation will disappear or lessen, according to many economists.

Easterlin is not just a single "way out" voice crying good news. While some other experts are less optimistic there is widespread agreement that the declining fertility rate makes possible some of the things he predicts.

"The potential for really dramatic developments is there. The demographics are good," said Wachter in a telephone interview.

The roots of the story go back to the immediate post-World-War-Ii era, when a baby boom began in the United States. The total fertility rate -- the number of children a woman will have in her lifetime -- jumped from 2.5, the figure of the 1930s and early 1940s, to 2.9 in the last half of the 1940s, and then continued mounting to 3.8 in 1957, when it began to tail off. By the early 1970s, it had dropped to 2.2.5, and today it has dropped to about 1.7.

This meant a huge crop of babies in late 1940s, 1950s, 1960s. In the mid 1950s, at the peak, over 4 million new babies were born a year, compared with 2.5 million in 1940. Today the figure is a bit over 3 million.

Many economists and social commentators say that when the big crop of baby-boom babies hit the schools and then the labor markets, it created many of the social problems others attribute to a special malaise of the American soul.

With a lot more teen-agers, there was considerably more competition for the entry-level jobs -- beginning jobs in the labor force for inexperienced, relatively unskilled and untrained workers -- and hence high unemployment, lower relative income. This in turn induced the insecurity and anxiety which sometimes lead to divorce or suicide.

Moreover, the teen-age and young-adult years in a person's life are also the period of crime. After that, people tend to commit fewer crimes.

According to calculations by Frank Graves, a student of crime statistics here, about two-thirds of arrests for all major violent crimes in the United States (forcible rape, murder, armed robbery and aggravated assault) involve people 15 to 29 years old.

As the absolute size of that age group swelled with the baby boom, there was a sharp upsurge in violent crimes (which have increased from 288,000 a year nationally in 1960 to 1.2 million today.

Now, however, the population of young people is going down sharply.

In terms of the job market, better prospects for young people also mean less distress for society. In the past, the economy has had more difficulty absorbing teen-agers who tend to be restricted to lower-skill jobs like manual labor and retail trades.

"A scarcity of younger workers will affect favorably their relative wages, unemployment rates and upward mobility," wrote Easterlin.

Arnold Packer, assistant secretary of labor, agrees, "The problems that we had of absorbing a big bubble of youth will no longer be present," he said.

Former secretary of labor Willard Wirtz, now chairman of the board of the National Manpower Commission, contends that Easterlin's and Wachter's projections could end up to be "a mirage" because of other possible changes in the labor market.

For example, Wirtz said in an interview, an upsurge of illegal immigrants could inflate the teen and young-adult labor force and offset gains from the demographic revolution.

Moreover, Wirtz pointed out, the percentage of women in the labor force has been rising rapidly. Today about half of all women over 16 are working or seeking work, a figure the Urban Institute recently projected will rise to 55 percent by 1990.

If the percentage of working adult women went up to 65 percent instead of 55 percent, it would bring an extra 6 million women into the labor force, in some cases in direct competition for jobs with the teen workers. This could cancel any improvements, Wirtz said.

Despite all these caveats, Bob Lerman, a youth labor market specialist at the Department of Labor, said, "The scarcity of youth labor is bound to help young black and young white workers . . . . By 1990, it would be surprising if the black unemployment rate didn't drop back to 20 percent."

This is still high, but the reduction from the current 35 percent rate would cut umemployment of black teen-agers from the current 325,000, to 225,000, not a small gain.

Another pleasant spinoff could be reduction of the welfare rolls, according to Mitchell Ginsberg, dean of the Columbia University School of Social Work. Many students have pointed out that, to a large extent, the rise in the rolls of the program of aid to families dependent children from 943,000 mothers and children in 1945 to 1.4 million in 1975 paralleled the postwar baby boom.

Since then, the rolls of welfare recipients have shrunk by about 1 million, and Ginsberg says a major reason is the smaller size of families in recent years.