They can query state databases and look for certain other red flags that someone is drug seeking, but there’s not really any way to know for sure. Amphetamines and benzodiazepines are very commonly abused and diverted. That being said, if somebody just wants to get high it’s generally a lot easier to buy drugs from somewhere else than to spend months waiting to get an appointment with a psychiatrist.
Psychiatrists are trained to spot drug seeing behaviors, and will never prescribe powerful mind altering drugs on the first few sessions. They have a responsibility against the patient, and experienced professionals have turned down many of these requests over the years. People who actively seek drugs are fairly predictable in their behavior, usually fit race, age and social groups. If a professional is in doubt they can always ask for a second opinion from another professional, or an agency that regulates drugs, that usually has social workers, psychologists and psychiatrists, even drug experts and drug withdrawal professionals.
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