enter (one's) mind
To occur to one suddenly. After that idea entered my mind, I was able to alter the experiment and finally achieve some success.
enter one's mind
Fig. [for an idea or memory] to come into one's consciousness; to be thought of. Leave you behind? The thought never even entered my mind. A very interesting idea just entered my mind. What if I ran for Congress?
enter one's mind
Also, enter one's head. Occur to one, come into one's consciousness. This expression is most often used negatively, as in It didn't enter my mind that he'd want to join us, or Run for office? It never entered my head.