In a surprise move apparently intended to get relations off to a good start in the new Reagan administration, West German Chancellor Helmut Schmidt yesterday became the first foreign leader to meet with the president-elect.

Schmidt, who is in this country on a private visit, had a farewell meeting and luncheon with President Carter and then, late in the afternoon, walked around the corner from the White House guest residence at Blair House and called on Reagan at the next president's temporary quarters on Jackson Place.

Schmidt's aides had telephoned Reagan's office in advance with a request that the chancellor be received and the president-elect agreed, the aides said. t

It had been widely assumed that Schmidt would meet with a number of Reagan advisers. But the prospect of a meeting with the new president was viewed as unlikely because Reagan had suggested publicly he was not inclined to meet with foreign leaders before his inauguration so as not to detract from President Carter's authority.He did not meet with Menachem Begin when the Israeli prime minister leader was here last week.

Reagan, however, has never specifically ruled out such meetings. Aides point out that when Begin was in Washington, Reagan was in California. This time the newly reelected leader of a country of crucial importance within the Atlantic alliance was close by. Several of Reagan's top advisers or associates, including former NATO commander Alexander Haig and former Nixon Cabinet officers George Schultz and Henry Kissinger, are also close friends of Schmidt's and might have had a hand in stressing the importance of at least a courtesy visit.

The two men met for 50 minutes. Pressed by reporters as he was leaving, the pipe-smoking Schmidt smiled and said only: "Yes, I'll tell you something. The governor, with his own hands, opened my tobacco box."

When Schmidt entered the White House Oval office at noon yesterday, President Carter told him that his visit at this time was "very helpful. Although sometimes the emphasis is on the differences between us, the important thing is the vast common commitments that we share."

"Right, right," answered Schmidt.

At the end of their 90-minute meeting, about a half-hour of which was conducted strictly between the two leaders with no other top officials included, Schmidt and Carter bade friendly and graceful public farewells in the White House Rose Garden.

Though it is widely known that the two leaders have had some serious differences and that their styles and personalities at times annoyed each other, both emphasized the "unshakeable" ties between the two nations and Carter added that: "I am always grateful for the personal advice he has always given to me."

Schmidt said to Carter: "To listen to you and to talk to you have always been a pleasure and has confirmed to us how close we are to each other." Schmidt also included U.S. soldiers in a long list of parting salutes, which might have been meant to wipe out a recent indirect swipe at the literacy of American GIs by Bonn's finance minister.

Both U.S. and West German officials suggested that the Carter-Schmidt meeting was mostly a wide-ranging talk about energy, the precarious situation in Poland, the Middle East and the war in the Persian Gulf. Left behind for the Reagan administration will be the thornier issues between Bonn and Washington, especially how an alliance should react to various Kremlin moves and how to restart stalled talks on limiting atomic arms, which is a major concern in Bonn.

Both U.S. and German officials also said the issue of whether Bonn would live up to its pledge to increase defense spending by three percent was essentially resolved, mostly by statements by Schmidt before he got here and also in talks yesterday between Schmidt and Defense Secretary Harold Brown. The Germans are expected now to come close to the promised figure but there was no pressure applied yesterday, especially since Bonn is one of the defensive stalwarts in the North Atlantic Treaty Organization. Rather, the point was made that Bonn is in a leadership role, as is the United States, and sometimes it, too, has to make tough decisions.

There were no decisions made on the question of several hundred million dollars Washington wants Bonn to lay out to help pay for improved facilities for U.S. soldiers stationed there.

After a breakfast meeting with German Foreign Minister Hans-Dietrich Genscher, Secretary of State Edmund S. Muskie spoke of Genscher's support of American interests "in ways that haven't fully been revealed yet," a possible reference to Bonn's efforts in Iran in the U.S. behalf.