“It’s been hand-to-mouth in this field, and now we have the core funding and infrastructure to really advance psychedelic science in a way that hasn’t been done before,” said Roland Griffiths, a neuroscientist at Johns Hopkins who will direct the new center. Dr. Griffiths said the new funds will cover six full-time faculty, five postdoctoral scientists and the costs of running trials. Among the first of those trials are a test of psilocybin for anorexia nervosa and of psilocybin for psychological distress and cognitive impairment in early Alzheimer’s disease.

“The one that’s crying out to be done is for opiate-use disorder, and we also plan to look at that,” Dr. Griffiths said.

Trials using psychedelics or other mind-altering drugs tend to have a similar structure. Participants, whether they have a diagnosis of PTSD, depression or substance abuse, do extensive preparation with a therapist, which includes a complete medical history and advice and information about the study drug. People with a history of psychosis are typically excluded, as psychedelics can exacerbate their condition. And those on psychiatric medications usually taper off beforehand.

On treatment day, the person comes into the clinic, takes the drug and sits or lies down, under continuous observation by a therapist, who provides support and occasional guidance as the drug’s effects become felt. In the Johns Hopkins trial that Ms. Petersen joined, participants wore eyeshades and headphones, lay down and listened to music.

“The first trip lasted six and half hours, and I didn’t move,” she recalled. A week later, she returned for another dose; each dose was about twice what recreational users take. Therapy using psychedelics or other mind-altering compounds typically involves just one or two sessions on the drug.

“I would be lying if I said aspects of my experience weren’t deeply challenging and upsetting,” Ms. Petersen said. “The therapist would grab my hand — would save me in a moment — and encourage me to adopt a posture of welcoming everything, like a meditation.”

The literature so far, from trials like these, suggests that psilocybin is promising for chronic depression and addiction, and that M.D.M.A., or ecstasy, can help people with post-traumatic stress, including veterans. Cannabis and LSD also have been tried, for addiction and other problems, with mixed results.