Government officials refuse to say whether they were taking any special precautions when Mr. Trump was taking the drugs. In conversations over the past week, which they would not hold on the record, several pointed to the stories surrounding Richard M. Nixon's last days in office in 1974. He was drinking heavily and talking to portraits on the walls, and his aides feared he was emotionally unstable.
His secretary of defense, James R. Schlesinger, a hawkish cold warrior, said he instructed the military not to react to White House orders on nuclear arms unless they were cleared by him or Secretary of State Henry A. Kissinger. (Mr. Schlesinger died in 2014, and Mr. Kissinger, now 97, has said that he had no knowledge of such an arrangement.)
If Mr. Schlesinger's account is true, it was "certainly extralegal," Mr. Narang said. There is no evidence that anyone around Mr. Trump, including Mr. Pence or Defense Secretary Mark T. Esper, whom Mr. Trump has reportedly frozen out of key decisions, had any enhanced authority while the president was on medication.
The "sole authority" tradition is unusual among the world's nine nuclear powers; even Russia requires two out of three designated officials to sign off on a nuclear launch. While the Constitution says that only Congress can declare war, the speed of bombers and missiles made clear during the Cold War that there would be no time to convene Congress or mount a defense. As a result, Congress began delegating to the president all powers to use nuclear weapons during Harry S. Truman's administration. He is the only president who has ordered a nuclear strike.
Officials from many nations felt the immense pressure surrounding such a decision during a simulation of a launch exercise conducted this year at the Munich Security Conference, the leading gathering of the West's national security officials. Volunteers donned virtual reality headsets and were put through the head-spinning flow of data that comes in as a president faces a 15-minute window to decide whether to launch ground-based missiles before they are destroyed.
There were tiny hints throughout that suggested there could be a false alarm, but the evidence was muddy.
"The last finger I would want on the nuclear button," said Hans M. Kristensen, the director of the Nuclear Information Project at the Federation of American Scientists, a private group in Washington, "is that of a president on drugs."
It is not a new problem: John F. Kennedy took powerful pain medications, though there is no evidence that his judgment was impaired during the Cuban Missile Crisis, the closest the United States and the Soviet Union came to a nuclear exchange.
But no one understands exactly how the drugs given to Mr. Trump interact. And according to scientists, the most common mood enhancements associated with dexamethasone are mania and hypomania, a euphoric state. The hallmarks of hypomania include inflated self-esteem, increased talkativeness, decreased need for sleep, racing thoughts, distractibility and absence of restraint to engage in activities that could invite personal harm.
Not surprisingly, the military imposes strict limitations on the officers who oversee the nation's nuclear forces. Known as the Personnel Reliability Program, it assures that the authority is vested in people "who demonstrate the highest levels of integrity and dependability" and whose behavior is observed "on a frequent and consistent basis." A 1991 study said thousands of nuclear personnel were decertified every year.
Peter D. Zimmerman, a physicist and former government arms scientist, said few things better illustrated the confused nature of the American effort to prevent a single individual from launching a nuclear strike than the "two-man rule" in nuclear silos, submarines, bombers and the nation's coast-to-coast atomic complex.
The rule requires the presence of two authorized people for any step involving access to the armaments or the launching of a nuclear strike. "No unaccompanied person ever approaches a nuclear weapon," Dr. Zimmerman wrote in a 2017 opinion essay. "It's a basic precaution against theft, misuse or sabotage."
But it does not apply to the commander in chief, whether in the Oval Office or at Walter Reed National Military Medical Center.
A president could misjudge the situation or become impulsive, Dr. Zimmerman noted in an interview. "And the consequences," he said, "would be horrendous."