Kelley Cutler was deeply skeptical when she took part in a monthlong pilot test of Reveri Health, a new digital hypnosis program, at Stanford University last year. The San Francisco social worker needed help quitting smoking, and only joined the program at her doctor’s urging.“I was thinking it was nonsense and was never going to work,” says Ms. Cutler, 44, who had smoked for 25 years. Her first hypnosis session, which took place in person with a clinician, was so anxiety-producing that she had to have a cigarette afterward.Reveri Health, one of a new generation of hypnosis programs and apps...