No. Alpha brain wave activity is a direct result of focusing one's consciousness in a way that relaxes brain activity, usually by focusing such attention, not on the brain, but on the breath or the hara, that point just below the navel, which has a reciprocating effect on the brain. The brain wave activity of ordinary people is usually in beta state, which is more active than when in alpha state:
"Think about complex problem-solving, for example. Most of the time, your waking hours are predominantly spent in the beta state. Beta is characteristic of alertness, concentration, focus and a logical and rational way of thinking. That’s the good news. The bad news is, beta is also associated with stress. Can you “think straight” when you’re stressed out? No. Can you think out-of-the-box creatively when you’re stressed… or when your mind is in logical/rational mode that automatically dismisses seemingly illogical solutions? No.
Alpha brain waves are associated with relaxed alertness, enhanced learning, creativity, peak performance, imagination/visualization and intuition.
That’s why, if you spend more time in alpha during the day, your problem-solving skills will improve."
» How to Generate More Alpha Brain Waves
So, you see, problem solving skills are better when there is LESS brain activity, not more. This is due to being able to see the solution to a problem directly and intuitively rather than forcing the mind to grapple with it.
Alpha waves are produced, not by thinking, but by meditating. Meditation is not thinking!