On this northernmost frontier of American political science, a state government has decided to see if money really will buy happiness.

One thousand dollar checks have been going out for a month to every man, woman and child in this oil-rich state. So far few of the recipients have even bothered to say thank you.

"I almost feel that I'm on welfare," grumbled Ron Moore, a 36-year-old realtor from Soldotna. "I've lived here 30 years and I don't see why I should rely on the state for subsistence." The giveaway "was very poorly planned," said Kathy Potter, an office supply sales supervisor here who plans to buy drapes with her money. "There should have been a better way to do it."

In the state Revenue Department at Juneau, Colleen Brown reported the givers are not blessed by the receivers, who only call to complain if their checks have not arrived. "We have received enraged and irate calls from just about everybody," Brown said. "You've never seen so many greedy people in your life."

So go the early days of Alaska's revolutionary scheme to share its oil taxes and royalties with its people, not through new roads or deeper harbors or any of the other pork barrel projects Washington is familiar with, but with blue and yellow checks instantly cashable at any bank. They are called "permanent fund dividends" and Alaska's experience with the idea so far may frighten away any future leaders elsewhere so bold and so rich as to attempt such generosity.

The giveaway has sent many Alaskan brains churning, not with sweet thoughts for Gov. Jay M. Hammond and the state legislature but with schemes to separate other Alaskans from their money. Police have reported several checks stolen from mail boxes. A full-page ad for the Alaska Bank of Commerce in the Anchorage Daily News said: "ONE THOUSAND DOLLARS! We'll help you make the most of it." A furniture store announced a "CHECK'S IN THE MAIL" sale: "Turn your permanent fund dividend into a water bed that you will enjoy for years to come."

Anchorage Times political reporter Ralph Nichols concluded after many discussions with his fellow Alaskans that, "With few exceptions they think it's the dumbest thing in the world, the only thing dumber being not to apply for it as long as they are giving it away."

This philosophy extends to the young and the unborn. The state's vital statistics bureau has been swamped with 1,000 requests a day for certified copies of birth certificates, necessary if parents are to claim $1,000 for each of their children. Any resident's child born up to midnight Oct. 15 may claim a check, prompting speculation that women with babies due about that time will flood hospital maternity wards and induce labor in order to make sure.

So far the Revenue Department has sent out 87,901 checks, each decorated with the state flag, which shows, appropriately enough, the stars forming the "Big Dipper." Brown said the state expects to send a total of $415 million in checks to the state's estimated 415,000 residents.

Alaskans don't seem quick to ladle out their new riches. Automobile and snowmobile dealers say there has been little upturn in business so far. Few charities claim to have benefited from the giveaway, though in some cases not for lack of trying.

The Fairbanks Environmental Center asked its members some time ago to donate all or part of their checks to the center, but so far fewer than 10 contributions have come in. The University of Alaska Foundation estimated it has received between 15 and 20 dividend checks.

Instead, with each check in the mail has come another family squabble. Jana Baumann, who works for the State Environmental Conservation Department in Fairbanks, said her daughter Sacha, 11, was quick to object when she learned her $1,000 was going into savings. According to her mother, Sacha said, "So and So gets to spend $200 of hers on school clothes and this one's going to camp and that one's going to Hawaii and why can't I have it in cash? "

Alaskan politicians who conceived the giveaway years ago wanted to demonstrate their faith in the people's ability to decide themselves how their money should be spent rather than building the usual political pet projects. The permanent fund has been created with about 25 percent of the state revenues from the Prudhoe Bay oil fields and other mineral resources. The giveaway checks were to come from half of the interest on the fund.

Hammond wants to give away even more. He has argued that all of the oil money, now about $4 billion a year, ought to go into the permanent fund. He said people ought to be paid from the interest and the amount of their checks reduced whenever state representatives voted for a large pork barrel project that drained money from the fund. Since the state income tax has been abolished, Hammond said, there was no other way to keep voters interested in the old question, "What are you idiots doing with my money? "

The checks sent out this year were originally due in 1980. But Ron and Patricia Zobel, married lawyers who arrived in the state in 1978, objected to the original plan to distribute payments on a sliding scale -- $50 for newcomers and up to $1,050 for old-timers. The Zobels successfully sued to stop that plan on the grounds that it discriminated unconstitutionally against new residents. The legislature decided to go ahead and give the same amount to everyone who had been in the state at least six months; adding the dividends that had not been paid since 1980. That brought the payment for everyone this year up to $1,000.

Ron Zobel said that like many of his fellow Alaskans he was never very happy with the idea of the government giving away cash. But now that the checks are arriving, the hate mail and threatening phone calls that accompanied his original suit have tapered off. The checks coming to himself, his wife, and their 15-month-old son will be invested in Alaska-oriented stock, he said.

Politicians here worry about what the giveaway will do to the state's relationship with the lower 48 states. They say they fear a mass inflow of American jobless, already a problem because of the widespread and somewhat erroneous impression that Alaska is full of job opportunities.

Under the current plan, Alaskans will each get $350 in 1983, $250 in 1984, and then the annual payments will begin increasing again at an unknown rate. Nearly every politician in the state expects the legislature to change the plan in some way next year. But the Revenue Department's Brown said, "They may find it very hard to get people to give up" the yearly dividend, no matter how ungrateful most have seemed for the money.

The checks have allowed a number of people to realize old dreams. Brown said her office received a letter from an elderly Eskimo man living in one of the coldest regions of the state's northern bush. "After thanking us profusely," Brown said, "He said that he was going to use the money to buy a refrigerator. I don't know if he was ribbing us or not."