In general, military rifles were not designed for optics until the M14. There are some ways to mount a scope on some (but not all) rifles with minimum gunsmithing. Sometimes it is satisfactory, sometimes not.
To consider an '03 Springfield (or '98 Mauser), to mount a conventional scope you have to:
1. Drill and tap the receiver -- which dramatically lowers the value of the rifle.
2. Weld on a new bolt handle (bending the handle may work) so as to clear the objective end of the scope.
3. Replace the safety -- the objective end interfers with the flag type safety.
4. Restock the rifle so as to put the eye in line with the scope. Adding a wooden spacer or a lace on pad may be sufficient, depending on how picky you are about looks and function.
In the end, you will have spent a couple of hundred dollars to convert a $600 military rifle into a $300 "sporter."