Why did Heisenberg remain in Germany when the Nazis came to power?
Heisenberg personally disapproved of Hitler's actions, but he sincerely hoped that Hitler's reign would be short-lived. Therefore, as encouraged by Max Planck, Heisenberg chose to remain in Germany to maintain the bright spots of German culture and science, with plans to facilitate their reconstruction after the Nazis' inevitable defeat. Moreover, Heisenberg was genuinely bound to the culture and the people and felt a sense of duty to remain there through the difficult times.
Whether or not these reasons justify the compromises Heisenberg had to make is the standard by which history must judge him. In short, he chose nation over humanity and physics over ethics. One approach to evaluating his decision is to consider the absolute morality of his actions versus the actual, practical effect his actions had. Morally and symbolically, Heisenberg was wrong to cooperate with such a morally repugnant regime and to promote the well being of physics at the cost of truth and justice. But the alternatives may have had little practical effect. Heisenberg was, after all, a physicist, and by remaining in Germany, he may have been able to contribute more good in this limited sense than he would have by acting according to absolute moral standards.
How did the youth movement affect Heisenberg's life?
At the time, the youth movement provided Heisenberg with a sanctuary from the disorienting state of Germany. Political and economic instability, as well as a general sense of disillusionment, contributed to a confused atmosphere for Germany's youth. They turned to each other for answers. Most of Heisenberg's youth movement activities consisted of expeditions during which the members would discuss philosophy, enjoy music and poetry, and generally bond with one another. As an older member, Heisenberg was usually a group leader who provided guidance to the younger boys.
Heisenberg's participation in the youth movement also had more lasting consequences. It taught him, for instance, to question traditional values, an attitude he would take toward the traditions of science as well. The philosophical tendencies of his companions also forced him to consider the broader consequences of his science–points that he often tended to ignore as a more utilitarian and pragmatic physicist. Heisenberg enjoyed his youth movement excursions immensely, and he continued to lead them into the 1930s. He would often refuse or simply neglect to think about his work while away, so that he would return after a month completely out of the loop–but likely with a fresh perspective on the new developments of physics.
How did anti-Semitism affect physics in Germany?
The most obvious problem caused by anti-Semitism was the loss of Jewish professors. Many were forced out of the country immediately. Those who were war veterans or had a stronger reputation held on a bit longer, but eventually either resigned or were forced to leave under increasingly harsh policies. Some notable non-Jewish physicists, including Erwin Schrödinger, resigned out of protest or fear of worsening conditions in the country. Those who were lost included celebrated researchers as well as the basic teachers needed to instruct the next generation. Heisenberg, with the help of Max Planck, was left with the task of finding replacements to keep even the most basic scientific community alive.
But beyond the simple removal of Jewish scientists, the Nazis had another aim as well: to remove the "Jewish spirit." This spirit was embodied by Albert Einstein, whose work the Nazis viewed as fictional and warped by his religion. Probably motivated in part by jealousy, former Nobel laureates Stark and Lenard attempted to discredit Einstein and his theory relativity completely. Made famous by their work as experimentalists, they also launched a crusade against the more general enemy of theory. Though Heisenberg insisted against mixing science with politics, he saw this crusade as an attempt to undermine the value of the science in which he believed, not to mention the validity of his own work. Fortunately, Heisenberg, with the support of nearly all the physicists still left in Germany, was able to lead an effective movement of resistance. But Stark and Lenard rose to considerable bureaucratic power at one point and inflicted damage that would take time to repair.