If memory serves me, the operating hypothesis for ADHD is actually that it's due to reduced activity in a portion of the brain that regulates and directs the rest, the theory behind most ADHD drugs being to increase activity in that portion of the brain in order to let it better regulate the rest of the brain.
Hence, the seemingly paradoxical effect of a stimulant making someone calmer. Someone with ADHD, unable to relax because of too much distracting, chaotic activity in their brain, may thus find that the drugs help them relax.
By crude analogy, it's the inverse of the way moderate doses of ethanol (a depressant) can make someone seem more active due to reduced activity in parts of the brain that provide inhibitions and impulse control.
From personal experience, I feel reduced amounts of gratification from doing mundane things. Mental stimulation is reduced, therefore I'm driven, in some cases like a motor, to find more stimulation. Activity in the brain , in the form of thoughts, is one way to increase stimulation. Stimulant drugs satisfies this need for stimulation, so we don't need to keep on thinking about stuff, like the meaning of life. My theory is that this need to race through thoughts is the mechanism for bad short term memory. Running through more thoughts means old thoughts are forgotten.
There are also different types of Adhd by the way. There's inattentive and hyperactive. My explanation probably fits inattentive ADHD since that's where my personal experience lies.
Hence, the seemingly paradoxical effect of a stimulant making someone calmer. Someone with ADHD, unable to relax because of too much distracting, chaotic activity in their brain, may thus find that the drugs help them relax.
By crude analogy, it's the inverse of the way moderate doses of ethanol (a depressant) can make someone seem more active due to reduced activity in parts of the brain that provide inhibitions and impulse control.