In this paper, Heisenberg wrote the mathematical rules to connect classical mechanics with quantum observations. If you like to track modern quantum mechanics to its read, this is the paper to read. The only problem is that it is not very easy to read paper, but you may seek help from this 2004 paper in arxiv - Understanding Heisenbergs magical paper of July 1925: a new look at the calculational details.
Dirac tidied up Heisenberg’s paper mentioned in 1.
Using newly discovered mathematical machinery (1 & 2), Dirac explored the hydrogen atom.
Schrodinger enters the picture in this paper.
Dirac is fascinated about how extensible the new mathematical techniques are.
This paper marks the birth of quantum electrodynamics. The topic eventually evolved into a vast field with contributions from Feynman, Tomonaga and Schwinger.
The cleaned, refined and extended version of Dirac’s mathematics came to be known as second Quantization and is useful to derive the collective state of many quantum particles acting together. It is one of the less explored areas of physics, despite many decades of research.
The subject says it all.
The above paper cites a physicist Darwin, who happened to be the grandson of biologist Darwin.
Darwin was born in Cambridge, England into a scientific dynasty, the son of the mathematician Sir George Howard Darwin and the grandson of Charles Darwin. His mother was Lady Darwin, Maud du Puy of Philadelphia, Pennsylvania. His elder sister was the artist Gwen Raverat, and his younger sister Margaret married Geoffrey Keynes, the brother of the economist John Maynard Keynes. His younger brother William Robert Darwin was a London stockbroker. Darwin was educated at Marlborough College and, in 1910, he graduated from Trinity College, Cambridge in mathematics.
Getting back to #6, why is the topic less explored? The answer lies in mathematics not being able to catch up with physics. When quantum mechanics was born, mathematics was a very advanced field due to three centuries of work from Newton, Euler, Lagrange, Gauss, Riemann, Fourier, Hamilton and all the way up to Hilbert, who was present at that time. Physicists drove on all cylinders and exhausted every mathematical tool including Hamilton’s quaternions. However, they apparently reached the limits of mathematical developments and could not handle infinite number of particles with the available methods. Since 1950s, every discovery on new ground state from the many body Hamiltonian appeared to have introduced new mathematical method as well. However, the approach does not allow a general solution.
We believe there is room for many centuries of new discoveries in this area. This will most likely take place in emerging Asia.