Others can give you more details than I can, but there's no way that the Germans are putting out a nuke a month in 1941. The German atomic bomb project was going in completely the wrong direction. The Nazis' racial ideology had also barred the German atomic bomb team from taking advantage of key breakthroughs in nuclear physics because they were made by Jews and Slavs. The Nazis also drove many of Europe's top physists into the arms of the Allies for the same reasons and the ones who had been unable to leave were arrested and/or killed.
The second reason is more important than the first: Many scientists left Germany, but plenty of good scientists stayed. So all the Nazis would have had to do is let the scientists refrain from saying aloud that a finding originated from a jew or slaw rather than forbidding to use that finding at all. Doesn't seem that hard to me.
The logisitcs and the cost of a German Manhattan project is a hard nut to crack, but since von Braun successfully completed a task that wasn't that much smaller, it's not quie ASB.
But how to accomplish this as early as 1941 ???
And how do the Germans prevent [edit] allies espionage?[/edit]
Having said that, if the Nazis had a working atomic bomb in 1941 and a way to deliver it, it would have changed everything.
Not quite everything: Sowjet casualties WERE in the order of magnitude of one Hiroshima or Nagasaki per month, even without nukes. The strategic advantage of building a bomb that is 10.000 times more deadly, but also 10.000 times more expensive, than a conventional one is overstated.
So to change the cause of WWII you really need to
- give Hitler the Bomb as early as 1941,
- prevent a faster Manhattan Project due to allied espionage and
- prevent the Germans running out of uranium after a couple of nukes.
So as I already said in earlier threads: None of the scenario's requirements is necessarily ASB, but the combination of them is.