They won't make the gun laws more restrictive. As even some German police spokesmen have already said, the laws that are currently in place are more than tight enough.
Especially with the hunting background, they just cannot ban handguns. The reasoning why every hunter is entitled to at least one handgun is the thing called "Gnadenschuß" -- when you've hit the game with the rifle, but only immobilized and not killed it. In this situation, the law says that a handgun is required.
Furthermore, fully automatic weapons cannot legally be purchased in Germany by civilians anyway, and semi-automatic weapons are also restricted.
Then you need to go through a LONG training (obtaining a hunter's license in Germany takes around two years of school training) and a lot of bureaucracy and exams before you are allowed to purchase a rifle.
How much more could this be restricted?
It's much easier - and quicker and cheaper - to talk to the "right" person in the "right" bar to get an illegal gun. And no law will ever prevent that sort of business.
Besides, no law could ever prevent a tragedy like this one from happening. Some people do not find a way to deal with the world as it is, and eventually they snap. If they don't use a gun, they might use a big truck and drive Amok instead of shooting. Or they lie fire to everything that comes in their way. Or they grab an axe and run through a pedestrian area. Or, or, or. There are infinite ways to run Amok, and none of them can be prevented.
And from what I've read today, this guy came from a "financially secure" family and "his parents bought him everything that he wanted". According to his teachers, he also was never mobbed, but even doing well in school and seemed to have been quite ambitious. Maybe nobody will ever know why he did what he did.
Spiegel Online wrote that he went for head shots and targeted mostly young women. Simple explanations would be that the preference for head shots could be related to zombie movies and first person shooters and the targeting of women could be related to sexual frustration or having been rejected by women that he was interested in.
Since he seemed to have been a quite intelligent person, he certainly was very aware of the consequences of his doing, so I think we can rule out an uncontrolled, spontaneous venting of aggression. I think this has been building up over a long time and he literally wanted to go out with blazing guns. Like somebody here said, this was a "suicide by cop", and he has probably fantasized about it for weeks or months before he had the opportunity (the unsecured gun) to realize it.
But no matter how long and deep this will be analyzed, the sad truth remains that tragedies like this cannot be prevented.
