If the status of the object with your run()/execute()-method should be saved in the objects fields between the executions, Quartz will not be very helpful, because it creates a new object for each triggering event.
My goodness. Talk about killing a gopher with a chaingun.
The class "java.util.Timer" should serve your needs nicely. You package your task as an class that implements Runnable, create a Timer, set the timer, and it takes care of firing the Runnable after specified delay.
If Quartz or not is a chaingun depends upon what need to be done. If it is simply a matter of delaying a one shot work a timer may be enought.
I found Quartz fairly simple to use and it is really good if you want to set up crontab like scheduling (using a quartz CronTrigger). (I.e. do this work every 15min between 7 am and 5pm Monday to Friday.)