Among those whose field was the study of the human mind, a widely held view was that Mr. Leary had gone off the deep end, giving their science a bad name in the process. Political concerns ran even deeper. Elected officials from the president on down feared that the youths of America were skidding anarchically toward a druggie cliff.

Stories abounded about suicides, murders and other horrors committed by young people soaring googly-eyed on LSD or having acid flashbacks. Not all of the tales proved to be true. Nonetheless, the federal authorities concluded that there was enough dangerous behavior for them to crack down.

Prohibitions against LSD and brethren hallucinogens, like psilocybin and mescaline, were codified in the Controlled Substances Act of 1970. In the 1980s, ecstasy — MDMA, short for 3,4-methylenedioxymethamphetamine — joined the list of Schedule 1 controlled substances, those deemed the most perilous.

Soon enough, serious scientific exploration of psychedelics dried up. Any dabbling in LSD, which Dr. Hofmann came to call his “problem child,” was called a career killer by many experimenters.

In recent years, though, mind-bending drugs have begun tiptoeing back into the research mainstream.

Essentially, modern scientists are picking up where their forerunners of the ’50s and ’60s left off. They are studying hallucinogens’ potential to help smokers kick the habit, to undo addictions to drugs and alcohol, to cope with cluster headaches and depression, and to deal with obsessive-compulsive and post-traumatic stress disorders. Institutions where such work is underway include New York University; Johns Hopkins University; the University of California, Los Angeles; Psychiatric University Hospital in Zurich; and Imperial College in London.

American research interest in psilocybin is especially keen. This is a psychoactive ingredient in the fungus family known as magic mushrooms. It helps that psilocybin carries little of the baggage that still burdens LSD, said Matthew W. Johnson, a professor of psychiatry and behavioral science at Johns Hopkins.

It may also help that scientists toil in a new environment for certain drugs. Marijuana, for instance, is a Schedule 1 substance. Yet it now has the legal blessing of some states.

Psilocybin and other hallucinogens, while not addictive, remain officially taboo everywhere. Researchers need a dispensation from the Food and Drug Administration, a licensing from the Drug Enforcement Administration and the approval of professional boards. If anything, today’s scientists want to be seen as the anti-Learys. Their experiments bear no resemblance to the freestyle acid-dropping of the ’60s. Patients are screened and prepped on what they may expect, and then closely monitored.

Given that death awaits us all, one intriguing pursuit is the use of psychedelics to alleviate deep anxiety — existential distress, some call it — in those for whom the end seems near. They are people like Sherry Marcy, a woman from Ann Arbor, Mich., who learned she had advanced endometrial cancer.

She succumbed to depression. Four years ago, Ms. Marcy, now 73, went to Johns Hopkins for two rounds of psilocybin treatment. The lift she received continues to sustain her.

“It wasn’t like it was psychedelic for me,” she said in an interview with Retro Report. “It just was me — back. I don’t know how it did that, exactly, except to broaden out. You know, it’s like you lift up your head and you take a good long look, and you start seeing things again.”

Scientists, too, are trying to figure out exactly how the drug helps ease despair. Nonetheless, they have observed lasting positive results, even spiritual awakenings, in some cases. If carefully administered, they say, hallucinogens can reorient patients’ perceptions of their place in the universe and pull them out of ruts of negative thinking. In a 2015 article in The New Yorker, a British researcher, Robin Carhart-Harris, likened the phenomenon to “shaking the snow globe.”

Studies have generally been on a small scale, and the results, while encouraging, are preliminary. Caution is required, Dr. Johnson of Johns Hopkins told Retro Report, for scientific rigor and because “there are potential dangers.”

Even so, Ms. Marcy, who is now free of cancer, says Timothy Leary got it one-third right. “The ‘turn on’ doesn’t have to be emphasized at all,” she said. “The ‘drop out’ is an absolute mistake. But the ‘tune in’ is crucial.”

“I tuned in,” she said. “Tuned in to the world, to me, to things I used to love, to my relationships, to my family. ‘Tune in’ is what it’s all about.”

CLYDE HABERMAN, a regular contributor to Retro Report, has been a reporter, columnist and editorial writer for The New York Times, where he spent nearly 13 years based in Tokyo, Rome and Jerusalem. Subscribe to our newsletter here and follow us on Twitter @RetroReport.

This article first appeared in The New York Times.