Excessive preoccupation with the (false) idea that one is in ill health. Hypochondriacs are generally difficult to reassure; their health worries may persist even after receiving a clean bill of health from a physician or a diagnostic procedure.

Here is a great resource on this disorder: http://my.clevelandclinic.org/disorders/hypochondriasis/hic_hypochondriasis.aspx

Example: “I know you did those tests and you didn’t find anything wrong, but what if you missed something? Can’t I see a specialist?”