Thank the prospective employer for taking the time to meet with you knowing how busy they are. Assure them you are aware of their difficult task of having to meet with numbers of anxious applicants and the responsibility of having to choose the best person for the job. You can casually mention how your special skills and talents could benefit the company but redirecting on his stressful task could enhance your personal skills in a time when putting yourself in his or her position projecting empathy can be a refreshing change to the normal applicant. This method always appealed to me when I had the job of interviewing applicants as it was never a favorable task and very routine with patent questions, etc. Be sincere in your appreciation for his time and empathize with his difficult job. He or she will appreciate your humble spirit and not put them in a position we never liked to be in. , it wouldn't hurt to even enclose a small token (not bribe) but something like a nice plant, gift certificate for a message, etc, sounds crazy but human kindness and empathy works wonders in this day of self-centered souls.
Make it brief and polite, and use stationery and pen. Don't beg for the job, just thank him or her for making time to interview you.
You don't write a thank you letter until you get the job. That makes life a lot easier don't you think?