For President Carter and West German chancellor Helmut Schmidt, their meeting at the seven-nation London summit this weekend is a highstakes encounter - especially for Schmidt.

It will be the first time the two4, the strongest and perhaps most puzzling personalities in the Atlantic alliance, will be seeing each other as heads of government and the meeting comes at a time of uncharacteristic difficulties in relations between their governments. There is also at least the hint of some strain between Carter and Schmidt in their personal views.

This has prompted some political commentators to predict a stormy encounter - A clash between two stubborn leaders, neither of whom can afford to back down on some key issues now in dispute between the U.S. and its most powerful European ally.

But in this West German capital, both German and American diplomats feel everyone involved in the summit, especially Schmidt and Carter, has an interest in making it a success. Each also favors strong Trans-Atlantic ties and is a modern manager and prynatist.

Schmidt clearly needs a boost for his sagging political prestige at home, and an international summit meeting, where he traditionally is an impressive participant, could provide it. Carter is viewed here as needing to polish his foreign policy image among his allies, especially after the generally unsuccessful intitial round of talks in Moscow in March on limiting nuclear weapons.

The hope, expressed by several officials, is that the two will come away from the summit and a private meeting impressed with the other.

Their ability to get along on a personal basis could mean much in finding common ground on key issues that now divide the U.S. not only from West Germany but also from much of Western European.

These include the export of nuclear technology, the question of how best to deal with East Europe on human rights grievances, and a wide range of economic policy issues.

On the surface, Schmidt and Carter seem to have much in common. Both are quick learners and dominant political personalities slightly on the conservative side of center and left-of-center parties.

But Carter is viewed as having a much greater dose of in-built ideology than Schmidt, and that is what worries many Germans.

Carter's fervor for curbing the spread of nuclear technology threatens one of West Germany's most important export industries and is a source of bitterness and confusion.

His outspoken attacks on human rights violations in Eastern Europe from a far away White House threaten, in the eyes of many Germans, what they see as the more delicate question; keeping the doors open between war-divided families scattered through East and West Europe.

Perhaps most important, however, Carter has come along at an unusual time in post-war West German history and at an especially difficult time for Schmidt.

Thirty-two years after the end of the war, the West Germans' powerful economy and enviable record of stability have earned them a respected voice in Western power councils. Schmidt clearly exercises it, sometimes abrasively.

Thus, West Germany no longer can be counted on to automatically acquiesce to American desires, whether on nuclear exports or paying for the added costs of keeping U.S. soldiers here.

On the other hand, the West Germans remain strong allies and have nowhere else to turn for their own long-term security. Any serious and prolonged falling out with the U.S., even if this initially had general support among the voters, would cause political problems for any government here.

So, Schmidt is arguing forcefully against what he sees as well-meaning but unfair American policies on nuclear power and wrong economic policies. But his political ability to carry out a prolonged fight with the U.S. or its President is risky.

Although only a year ago, Schmidt was viewed as the most dominant leader in the West, he and his party narrowly escaped defeat by conservative forces in October's federal elections.

Since then, his coalition of Social Democrats and Free Democrats has had a bewildering array of political disasters - lost local elections, party-in-fighting, local financial scandals, and assorted other mishaps. Some were Schmidt's errors, but most are blamed on poor organization of his party.

Today, few observers show confidence that Schmidt's government will last beyond next year's state elections. If the chemistry between Carter and Schmidt remains bad, or if the chancellor is forced to capitulate over the crucial nuclear issue, his chances of retaining power will be even less.

Few German or American observers see anybody around who could suitably replace Schmidt at this stage, including opposition leader Helmut Kohl.

Carter and Schmidt met once before, briefly, during a Carter trip to Europe in 1973 when Schmidt was Finance Minister under Chancelor Willy Brandt.

Several factors have contributed to the personal strains between Schmidt and Carter, though both German and American officials insists that these have been exaggerated.

Schmidt's recent political batterings and his inability thus far to recapture his leadership stride has sparked recurrent rumors that he is depressed, ill or resigned to defeat. "Schmidt is in a foul mood," one U.S. official said, "but not because of us."

Indeed at the moment Schmidt seems like two men, one in trouble at home and inexplicably not yet counterattacking forcefully, the other the kind of chancellor who is almost certain to rise to the occasion at a summit.

Schmidt, who has a habit of saying things to newmen he ultimately regrets, let it be known that he favored former President Ford during the U.S. campaign, mostly because he was a known quality. 'Previously, he has alrways capitalized on his excellent relations with U.S. Presidents but has not yet seen Carter, whom four other leaders at the summit have already met. Then the German Ambassador in Washington, perhaps inadvertently, was left far back in line at the White House.

Feelings were frayed both in Bonn and Washington when both sides resorted to lecturing each other on economics, an area where Schmidt, a former Finance Minister, feels especially secure.

The crucial issue, however, involves Carter's efforts to halt part of Bonn's almost $5 billion deal with Brazil for eight nuclear power stations plus fuel reprocessing and uranium enrichment technology. It is the latter two processes - which yield material for atomic bombs unless tightly controlled - to which the United States objects.

Just before Carter's nuclear policy statement early in April, the Germans made it known publicly that they were going ahead with plant blueprints to Brazil.

Just after Carter pro-nouncements on curtailing U.S. fast-breeder reactors, Bonn announced a new energy plan involving continued research on these fuel-creating devices.

Neither of these developments was unexpected, but the timing was probably viewed in Washington more as an affront than coincidence.

Though Bonn has suggested it would probably not make any more deals like the VBrazilian one, Schmidt has stressed that Germany will only refrain if all the world's industrialized countries do likewise.

The nuclear question, thus is both the most crucial, and the one for which there is virtually no solution in sight.

Though some German critics of Bonn's policies call the Brazilian deal the wrong sale at the wrong time to the wrong country, the government view is that the U.S. cannot by unilateral action attempt to thwart the legitimate striving of other fuel-short and uranium-shor countries for atomic power and secure fuel supplies.

Bonn views this as counter-productive, eventually forcing nuclear have-nots to seek such technology on their own, without even the safeguards that Bonn claims are so stringent in the deal with Brazil.

Officials here are not confident of Carter's indications that certain countries will have a guaranteed supply of atomic fuel from the U.S. if they forego exporting technology. They pointed to the recent U.S. tactic of withholding such shipments as a sign that the policy would be one of threatened embargo at any time.