Primarily it was Max Planck who introduced the quantum theory later it was developed by several other scientists.
Not sure what you mean by "derive" quantum theory; that's along the lines of "deriving" gravity. In our Universe, quantum theory is the only one we've developed that matches experimental evidence. In all cases, quantum theory was developed mathematically simply because no other explanation existed that would match what occurs in our Universe. Whether we like it or not, whether we really understand it or not, we are in a Universe that obeys quantum theory.
Classical free electron theory could not explain many physical properties. In 1928, Sommerfeld developed a new theory applying quantum mechanical concepts and Fermi-Dirac statistics to the free electrons in the metal. This theory is called quantum free electron theory.
Schrodinger, who created the schrodinger's cat theory.
Vinton Cerf from USA developed the Internet and TCP in 1973
actually einstein developed one of the earliest parts of quantum mechanics: the theory of the photoelectric effect. he worked directly with many of the scientists that later developed the complete theory of quantum mechanics and the mathematics to solve its apparent paradoxes to get usable predictions from the theory. later he rejected it due to it being nondeterministic, not because he didn't understand quantum mechanics but because he did understand quantum mechanics. he then tried to combine quantum mechanics and general relativity, hoping the resulting unified field theory would resolve the nondeterminism of quantum mechanics, resulting in a single fully deterministic theory of everything.
Quantum Mechanics was invented by Max Plank - and Einstein had nothing to do with it, in fact Einstein was uncomfortable with Quantum Mechanics for the entirety of his career.
Heisenberg and Schrodinger developed the electron cloud model using quantum mechanical probability functions to determine the the regions, or clouds, in which electrons would most likely be found outside of the nucleus.
Stephen L. Adler has written: 'Quantum Theory as an Emergent Phenomenon' -- subject(s): Quantum theory 'Quaternionic quantum mechanics and quantum fields' -- subject(s): Quantum theory, Quaternions, Mathematical physics, Quantum field theory
Rudolf Haag has written: 'Local quantum physics' -- subject(s): Quantum field theory, Quantum theory 'On quantum field theories' -- subject(s): Quantum theory
Heinrich Saller has written: 'Operational Quantum Theory I' 'Operational quantum theory' -- subject(s): Mathematics, Quantum theory
The original founder of quantum theory was Max Plank. The basic theory has been improved upon many times but there hasn't been a 'Modern Quantum Theory' that replaces the old.