"THE Search for Alexander," which goes on view today at the National Gallery of Art, ends in disappointment.

You may seek Alexander -- the conqueror of empires, the often-wounded warrior, the hero, the explorer -- among these mostly minor objects, these marble heads and grave goods. But you will not find him.

Despite its wreaths of hammered gold, its extraordinary jewelry, its graceful silver vessels and ancient coins and weapons, "The Search for Alexander" does not fulfill its promises. This large and lavish loan show seems hollow at the core.

The gallery, we know, is great at "blockbuster" exhibits, and this one, like all others there, is splendidly installed. The niches and pilasters suggest antique temples; the cases glow like jewels; minor objects stand on what the viewer takes to be pillars of red marble. The slide show that introduces the exhibition is computerized. It opens with a bit from the movie "The Black Stallion." Many curious photographs -- of ancient battle sites and comic books and Richard Burton acting -- add flash to the display.

But this is not a TV special, though one has been planned. Nor is it a lecture, a movie, or a picture book. It is meant to be a show of ancient works of art, arranged in a sequence of rooms.

The first gallery contains life-sized heads of stone and bronze which, we are told, are portraits of the conqueror. Ancient coins, some of which bear his likeness, are displayed next. The small figurines of Herakles we then encounter display the same features: The human Alexander (356-323 B.C.) has by now become a god. The gallery that follows contains the fine gold jewelry that is the highlight of this show. The next rooms move us on to the art of his homeland, Macedonia. These terra cotta figurines, silver drinking vessels, bronze burial urns and lanterns do conjure that provincial land. But where, the viewer now wonders, is the warrior Alexander who wished to rule the world?

Where is his horse, Bucephalus, for whom he named a city? Where is the crystal casket in which his body lay in state for 700 years? Where is the copy of the "Iliad" he kept beneath his pillow? This exhibition does suggest his drinking bouts, his wealth and his propoganda, but what about his tactics? What made Alexander -- who died at 32 and never lost a battle -- a leader without peer? Why did his Macedonians follow him to India? How did he supply them? Where are the 16-foot-long spears with which he armed his infantry? One cannot bring to Washington the headless men and Amazons, the talking trees and dragons of Alexandrian legend. But why is there no trace of Darius, the Persian kind he relentlessly pursued?

There are a dozen figures here -- of Herakles and Pan -- all of which, the labels say, portray Alexander.But many date from Roman days, and when these works were carved or cast, Alexander had been dead perhaps 500 years. All these "Alexanders," it is suggested, are copies made from copies of lost portraits made from life. Such claims evoke suspicions. These broken bronze and marble heads from Lycia and Rome, Tivoli and Sparta, may accurately portray the features of the conqueror. But how are we to know?

"The Search for Alexander" begins in the present. The introductory slide show, with its sound track and its movie stills, is there to cast the spell of his still-living legend. Only in the final room -- 175 objects later -- is the viewer told that "no object known to have belonged to Alexander the Great has yet been unearthed."

One wonders -- though, of course, one knows -- why this show was not titled "Macedonian Art" or "Grave Goods from Vergina and Associated Objects." This frustrating exhibit is in many ways a tease.

Still it does present us with small objects of great interest. It reminds us once again that the art history surveyed in Washington's museums is edited severely. True, there are no life-sized marbles in this show, no carvings from the hands of Phidias or Myron, Lysippus or Praxiteles. But this remains the first large exhibit shown here to offer us a glimpse of Hellenistic art.

That is its main virtue. The art of ancient Rome, of the Florence of the Renaissance, even the bronze statues that decorate our parks, are heirs of these small objects. For it was Alexander, Aristotle's student, who more than any other man carried to the world's ends the glory that was Greece.

Nowhere is the debt we owe that proselytizing warrior more explicitly apparent than in the Derveni krater, a three-foot-high bronze burial urn -- thought to date from the 4th century B.C. -- unearthed near Thessalonike in 1962. The krater is so richly wrought and so profusely decorated it seems as first glance almost vulgar. But examine it more closely and it seems the most impressive, and the most encyclopedic, object in the show.

Beasts of all descriptions -- serpents and gazelles, lions, boar, and sheep --stroll about its rim. The krater tells the story of young Dionysos and his orgiastic rites. The right leg of the god is indolently draped over Ariadne's thigh. Graceful numphs beside him rend their veils in frenzy or tear fawns limb from limb -- while a number of their sisters, understandably exhausted, doze beside the handles of this large metal jar. Look closely at their faces. They uncannily resemble larger drowsing goddesses that Michelangelo would carve -- some 2,000 years later -- for the Medici tomb.

Time and time again that eerie sense of millennia compressed surges through this show. The dimes and quarters in your pocket clearly are descended from the coins of ancient Greece. That drinking cup of silver from Tomb III at Vergina seems a work of almost Jeffersonian refinement; those ears of golden wheat -- literally golden -- are wholly naturalistic; that small bronze Aphrodite, her hair wrapped in a turban, seems no more antique than a sculpture by Maillol. She is one of the most beautiful objects in this show. s

Other pieces here seem, in contrast, almost clunky. No one would describe those terra cotta erotes (small figurines) or that small bronze Poseidon as major works of art. In many of these pieces, as in Alexander's life, the gracious and the brutal are easily combined. Study, for example, that silver deer's-head drinking cup (called a rhyton). It is a work of awesome beauty, yet heavily armed soldiers hack at one another in battle round its rim. It is wrong, this piece reminds us, to think of Alexander as some gracious touring gentleman spreading Greek refinement. True, he read his Homer, but he burned Thebes to the ground. He taught his men to love him, yet when drunk could shove a spear through Cleitus, his buddy. The art that he loved most of all was the art of war.

Though posterity forgives the atrocities of victors, he was, of course, part butcher. The images from Persia, Italy and Hollywood with which the show begins tend to stress his genius, his wisdom and his courage. The remembered Alexander is part saint and part sage. Rarely in those photographs do we sense the stench of corpses. Yet death and death's accouterments are at the center of this show.

The first old objects that one sees, those Greek and Roman portrait heads, all seem smoothed and flattered by funerary politesse. That gallery of heads calls to mind a graveyard. This show's Alexander does not sweat or suffer. He thought himself the son of Zeus, and in almost all the statues here we see the great commander remembered as a god. Gods, of course, don't die; but were it not for death, the objects in this show would not have survived. The gold would have been melted down, the terra cottas broken, the ancient paintings lost. It was Macedonian custom to give their dead a party. The nobles of the region often drank competitively. How nice to spend eternity reclining on a banquet couch, drinking undiluted wine from a cup of silver. Almost all the precious things in this exhibition come to us from graves.

The exhibition closes with a golden chest and a golden wreath discovered just three years ago in the village of Vergina in an unrobbed tomb. Some historians, but not all, date this royal tomb to Alexander's lifetime, and contend that the golden chest once contained the bones of Philip Ii, King of Macedonia, Alexander's father.

Alexander the Great never made it home. He died in Babylon, of fever. Though his corpse survived for centuries, it too has been lost -- like so much else about the man. A wondrous mist of legend swirls about him still. Dissipate that mist, as this show pretends to do, and you will discover that there is very little there.

Alexander, even so, is more fortunate than many other ancient conquerors. Consider, for example, poor Hermanric the Ostrogoth, who, so Gibbon tells us, conquered most of Europe 1,600 years ago. Hermanric, in his own way, was as great as Alexander, whom he much resembled "with this singular and almost incredible difference" -- Alexander's exploits were "supported by the vigor of youth." The Ostrogoth's were not. Hermanric, whose dominions "extended from the Baltic to the Danube" started his conquests at the age of 80. He finished at 110. You might think that sufficient to protect him from oblivion, but, of course, it wasn't. The real Alexander may never be recovered, but at least his fame survives.

The gallery's exhibit -- on view in the East Building -- was sponsored by the National Bank of Greece and Time Inc. Mobil paid for the slide show. tJ. Carter Brown, the gallery's director, chose the objects shown, more than half of which are loans from greek state collections. The exhibition will travel to Chicago, Boston, San Fransico and New York after closing here on April 5, 1981.