"It's been only half jokingly said that today a third of GDP is attributable to quantum mechanics," -- former Lockheed CEO Norm Augustine.I've heard the one third or 30% of GDP figure from time to time, but have never seen a detailed analysis. A list of modern technologies that arose from quantum mechanics would include: transistors, microprocessors, lasers, sophisticated chemistry and materials science, nuclear energy, memory chips, hard drive storage, LEDs, LCD displays, etc. These certainly account for a significant fraction of GDP.
Estimates of expenditures on communications and information technology alone in developed countries are typically in the 5-10% GDP range, which provides a lower bound. While the actual figure may be less than 30% it is certainly substantial. See here for a history of physics contributions to information technologies.
The huge (but poorly understood) impact of quantum mechanics on modern life is an example of the tremendous long term impact of fundamental research. There is every reason to think that increased world research expenditures would enhance productivity and quality of life, with very high ROI. However, there is little careful thinking about the "right" level of research investment as a fraction of GDP. Instead, we get:
Perhaps the most amazing aspect of the history of quantum mechanics is not its technological and practical impact, but rather how it led to deep changes in how we think about the universe. See, e.g., Two slit experiment, Bell and GHZ, Weinberg on quantum foundations, and On the origin of probability in quantum mechanics.
Early pioneers doubted whether humans were smart enough to understand quantum physics:
[Wigner] Until 1925, most great physicists, including Einstein and Planck, had doubted that man could truly grasp the deepest implications of quantum theory. They really felt that man might be too stupid to properly describe quantum phenomena. ... the men at the weekly colloquium in Berlin wondered "Is the human mind gifted enough to extend physics into the microscopic domain ...?" Many of those great men doubted that it could.Quantum mechanics, which made possible the modern age, is nevertheless only understood by at most a fraction of a percent of the population. See also Psychometric thresholds for physics and mathematics, Chomsky: genetic barriers to scientific progress, and Beyond Human Science.
Beyond Human Science: [This Ted Chiang short story envisions a future in which science has become the province of genetically enhanced "metahumans" -- leaving non-enhanced humans to gape from the sidelines.]
... imagine if research offered hope of a different intelligence-enhancing therapy, one that would allow individuals to gradually "up-grade" their minds to a metahuman-equivalent level. Such a therapy would offer a bridge across what has become the greatest cultural divide in our species' history ...
We need not be intimidated by the accomplishments of metahuman science. We should always remember that the technologies that made metahumans possible were originally invented by humans, and they were no smarter than we.