//most simple algoritm: return rooms where there is no reservation/lecture in the requested time-period
public function index?(requested_b_time, requested_e_time){
 $rooms = Room::join('reservation', 'room.id', '=', 'reservation.room_id')
  ->select('room.id', 'reservation.begin_time', 'reservation.end_time')
  ->whereDay('begin_time', requested_b_time->format('d')) //day equal to requested begin day
  ->whereDate('begin_time', '>=', requested_b_time)       //begintime after or at the requested begintime
  ->whereDate('end_time','<=', requested_e_time);         //endtime befor or at the requested endtime

 return $rooms;???