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Most physicists consider Einstein and Max Planck the fathers of quantum mechanics.

https://en.wikipedia.org/wiki/Father_of_quantum_mechanics

The book Einstein and the Quantum details his contributions to quantum mechanics, but because of his objections to the final theory, he's not credited much for it. Here's a summary by a StackExchange poster.

>His Law of the Photoelectric Effect (a misnomer - it should REALLY be called, the Quantization of the Radiation Field).
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>His Paper on the Specific Heat of Solids (1906)
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>His Paper on Quantum Vibrations (1907) ...Mind you he was the ONLY physicist in the world seriously working on quantum theory - even Bohr thought his idea of quantized energy (i.e. photons) was silly, given how great thinkers like Poisson and Maxwell had "proven" that light was a wave. Not a SINGLE notable scientist believed in Einstein's 1905 paper until at least the First Solvay Conference of 1911, and even then the vast majority were 'quantum skeptics.'
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>In 1909 Einstein was the first to show that statistical fluctuations in thermal radiation fields display both particle like and wavelike behavior; his was the first demonstration of what would later become the principle of complementarity.
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>1916, 1917 marks Einstein's most underrated paper. After finishing his magnum opus, General Relativity, he turned to the interplay of matter and radiation to create a quantum theory of radiation. He once again based his arguments on statistics and fluctuations. Bohr introduced a crucial new concept called stationary states in his 1913 paper on hydrogen but major features of Bohr's model could be interpreted as absolute nonsense because, according to electromagnetic theory, the electron would radiate intensely, emitting a broad spectrum as it crashed into the nucleus. Here we see contradictions in classical laws, and yet major properties of Bohr's hydrogen model rested on those laws.
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>Einstein, always the original thinker, didn't take as his starting point the well-known field for thermal radiation given by the Planck radiation law. Instead, he assumed that the atoms are in thermal equilibrium and then deduced the properties of the radiation field required to maintain the equilibrium. Guess what? The field turned out to be given precisely by the Planck radiation law. He manages to create quantum effects (stimulated and spontaneous emission) from most classical principles. He uses Wien's displacement law, the canonical Boltzmann distribution, Poynting's theorem, and microscopic reversibility - all classical. The sole quantum idea was the concept of stationary states. And yet from these elements, he's the first to create a complete description of the basic radiation processes and a full description of the general properties of the photon. In his 1917 paper, he creates novel and elegant derivations of Planck's radiation law as well as a proof of Bohr's frequency rule. In it, among many other things, he answers the question of how a gas of atoms maintain the populations of its stationary states in equilibrium with a radiation field.
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>The aforementioned novel concept of spontaneous emission, which embodies the FUNDAMENTAL interaction of matter with the vacuum, is a brilliant, Nobel-Prize worthy achievement. Why? Spontaneous emission sets the scale for ALL radiative interactions. The rates of absorption and stimulated emission, for instance, are proportional to the rate for spontaneous emission. Spontaneous emission can be viewed as the ultimate irreversible process and the fundamental source of noise in all of nature. With the development of cavity quantum electrodynamics - the study of atomic systems in close-to-ideal cavities - in the 1980s, the physical situation was profoundly altered. In such cavities, spontaneous emission evolves into spontaneous-cavity oscillations. Although the dynamical behavior is totally altered, the atom-vacuum interaction that causes spontaneous emission sets the time scale for that evolution. It is first in Einstein's 1917 paper that the photon is demonstrated to possess all the properties of a fundamental excitation, and therefore it is quite clear that his radiation paper played a seminal role in the eventual creation of quantum electrodynamics.
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>Apropos the second brilliant creation of his 1917 paper, stimulated emission of radiation, we see the first genesis of the laser. Stimulated emission underlies the basic mechanism of the laser and, by extension, laser cooling; his analysis of momentum transfer in a thermal radiation field can be immediately applied to atomic motion in a laser field. If the spectral width of a thermal field is replaced by the natural line width of the atom, Einstein's viscous damping force would give rise to the phenomenon known as optical molasses. This fundamental process of laser cooling was rediscovered by the atomic community in the 80's. Of course, you need Quantum Mechanics for a full realization of all the mechanisms of radiation, but papers like this are seminal contributions to what would eventually become QM.
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>Einstein's theory of radiation provided a complete characterization of the particle like properties of the light quantum and, in retrospect, he was within an arms grasp of working out the statistical mechanics of these particles. Given that his 1905 proposal for the energy quantization of radiation was based on the analogy between entropies of thermal radiation and a system of particles, it is surprising that Einstein didn't extend his method of reasoning to derive the Planck law by treating photons as indistinguishable particles. He was VERY close, and it is quite apparent that Bose himself did not realize he had done anything novel.
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>On the Quantization of Chaos (1919): In it, Einstein was the first to point out the fundamental problems that arise when one applies classical chaos theory to quantum states (a paper 50 years ahead of its time as this is a problem we have only now began to fully grasp): http://boulderschool.yale.edu/sites/default/files/files/Einstein_chaos.pdf
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>2. Fast forward to 1924 and Einstein, not Bose, applied the reasoning in Bose's treatment of photons as indistinguishable particle to a gas of indistinguishable atoms thereby creating Bose-Einstein statistics, and later, Bose-Einstein Condensation. Subsequently, Einstein theorized Bose-Einstein condensation, a work for which 6 Nobel Prizes have been given. Einstein was 45% of the way to the Schrodinger Equation. It was only after Schrodinger had read Einstein's paper that he derived his equations governing the wave function.
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>3. Einstein was the first to conceive of ghost fields as probability densities, a concept which he applied to a gas of photons (i.e. probability waves). Max Born essentially took the idea verbatim and applied it to electrons. Born always acknowledged this.
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>4. EPR Paradox Paper: the first paper to show how quantum entanglement emerges from the QM's equations.
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>*Einstein's work on wave-particle duality led directly to De Broglie's thesis on matter waves, and it seems unlikely De Broglie would have conceived of it without Einstein.
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>Einstein is pretty much the father of early quantum theory, and is one of the co-founders of modern Quantum Mechanics. The three major statistical systems governing the microscopic realm are: Fermi-Dirac Statistics, Einstein-Bose Statistics, and the Boltzmann Statistics. He would rightly be regarded as a legend for his work on BEC alone, and yet he contributed massively to Quantum Mechanics. Kindly check out his paper on the quantization of chaos, it's absolutely brilliant and shows how indispensable his thinking was to the development of QM.

It's a book on the math of GR (Differential Geometry by Erwin Kreyszig). Pretty great book and it's like 12 bucks on amazon.

I’d recommend reading a text on linear algebra. Hoffman is pretty thorough: Linear Algebra (2nd Edition) https://www.amazon.com/dp/0135367972/ref=cm_sw_r_cp_api_oZkMAb4NH15B3

I made this based on a post I saw recently

Quantum Physics for Babies https://www.amazon.com/dp/1492656224

It should be noted that renormalization now has a rigorous mathematical foundation.