There are two schools of thought on the obstacles in the path of the Middle East peace process now that Anwar Sadat is gone.

One is that the serious trouble starts on April 26, the date Israel is due to evacuate the last third of Sinai. The new Mubarak government, having meanwhile stood firm on Palestinian autonomy proposals that Israel finds unacceptable, will then put relations with Israel on a minimal, cool, formal basis, in an effort to assuage discontent at home and to buy Egypt's return to the Arab fold.

This will leave Israelis in a black mood feeling that they have surrendered territory and a security buffer for an empty peace. It will curdle even further their taste for compromise in dealing with the Palestinians.

That's what the optimists feel.

The pessimists feel the serious trouble will start well before April 26: the Begin government, anticipating the above scenario, will have great difficulty completing the Sinai withdrawal without being much more sure of President Mubarak than is now the case. No verbal assurances he could conceivably provide will help.

So the Israelis will devise some sort of test of Mubarak, say, a tremendous whack at PLO forces in Lebanon. If, despite it, Mubarak stays on the normalization track, the Israelis will complete their withdrawal, and if he gets off, the Israelis will not. In either case, the Egyptians will have no incentive to satisfy Menachem Begin on the Palestinian issue, since to do so would block Mubarak's grasp for domestic consensus and Arab company.

For what it's worth, I find myself among the pessimists. Israel has an immense national investment, and Begin an immense personal one, in consummating the Israeli-Egyptian peace treaty. But a case can be made that if consummation is to be incomplete, better that it happen before all the territory has been lost--if it can be portrayed as Egypt's fault.

Egypt and Mubarak also have large investments in the treaty, but not of the same gravity. After completion of Israeli withdrawal--if necessary, perhaps, even before--a deadlock on the Palestinian issue may have a certain appeal.

In a word, it is foolish for the Reagan administration to rely just on demonstrations of military reach and readiness to bring about a post-Sadat calm in the Middle East. The crisis there has a military dimension but is primarily political and centers on the Palestinians. That April 26 Sinai deadline was hanging out there anyway, and it was going to compel certain choices on the Palestinian question no matter who was ruling in Cairo.

The minimal American requirement is to get that planned multinational peace force out into Sinai pronto to ensure that, no matter what the state of Israeli-Egyptian political relations, military instability does not return to that front. The United States accepted such an obligation at Camp David.

After that, the administration had better get cracking and figure out how to keep some sort of negotiating process alive. Camp David has the virtue of existing, but Begin has cast a dark shadow over its future by his parched approach so far to the autonomy talks and by his expansive policy of Jewish settlement in the West Bank.

A number of Americans think it's wrong to yield up Camp David without the Reagan administration's first making its own big push to make it pay off further. The Europeans favor their own salaam to the PLO. The wider diplomatic community's clear favorite seems to be the Saudi eight-point plan, a wispy but suggestive outline that would, its partisans argue, sustain the large amount of additional work needed to make it into a worthy diplomatic vehicle.

But the prime need is not the right plan. It is, quite simply, for the friends of the two principals to undertake to impose a fair and secure settlement, the United States for the Israelis and mainly the Saudis for the Palestinians.

For Ronald Reagan it will take a difficult combination of firmness and assurance, including perhaps an offer of a concrete security guarantee. It entails a momentous political decision, and at this point he does not appear even close to considering it.

Why would he? If he is not impressed by the argument that American interests may otherwise suffer, he might consider the openings that a non-decision offers to Moscow. It might also make a difference to Ronald Reagan, considering that he is Ronald Reagan, that by going about it the right way he could do a great service to Israel, a nation he cares about deeply.