A flight instructor reported their student solo pilot lost control of the aircraft during landing resulting in a runway excursion.

Narrative

I sent my student pilot solo to the practice area this morning for their third solo; but their first time leaving the D airspace. Upon returning to the airport they landed on runway XX; in the touchdown zone; but veered to the right and then overcorrected and veered off the runway to the left. The student stopped in the grass area about 50ft to the left of the runway and immediately cut the fuel mixture and the plane came to rest. The student was not injured; the plane has no apparent damage; and they did not strike anything on the airport. The student has around 130 hours in total time; and was well prepared for their solo flight today. The occurrence may have been caused by their mental state going into the flight; over use of braking and applying too much rudder upon touchdown.To prevent and correct going forward; I will be more careful with student's mental state prior to solo. In addition; the student will receive more structured training and have a set plan in place to correct their rudder and braking while landing.