Quantum mechanics is quite a broad term. Perhaps it is best to start approaching it from the division into:
- non-relativistic quantum mechanics: obviously the simpler one, and where you should start
- relativistic quantum mechanics: more advanced, and arguably "less useful"
Key experiments that could not work without quantum mechanics: Section "Quantum mechanics experiment".
Mathematics: there are a few models of increasing precision which could all be called "quantum mechanics":
Ciro Santilli feels that the largest technological revolutions since the 1950's have been quantum related, and will continue to be for a while, from deeper understanding of chemistry and materials to quantum computing, understanding and controlling quantum systems is where the most interesting frontier of technology lies.
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- Bra-ket notation
- Classical limit
- Classical mechanics
- Condensed matter physics
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- Correspondence principle
- Derivation of the Klein-Gordon equation
- Dirac delta function
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- Dual vector
- Einstein solid
- Entropy
- Half-life
- Hilbert space
- History of quantum mechanics
- Inward Bound by Abraham Pais (1988)
- Lebesgue integral of is complete but Riemann isn't
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- Matrix mechanics
- Maxwell's equations in curved spacetime
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- Non-relativistic quantum mechanics
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- Perturbation theory
- Phase-space formulation
- Position and momentum space
- Quantum computers as experiments that are hard to predict outcomes
- Quantum electrodynamics
- Quantum key distribution
- Real world applications of the Lebesgue integral
- Relativistic quantum mechanics
- Richard Feynman
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- Tobias J. Osborne
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- Wheeler-Feynman absorber theory