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Explore quantum mechanics through this comprehensive lecture series that progresses from fundamental concepts to advanced topics over more than 28 hours of content. Begin with the historical foundations by examining blackbody radiation, the ultraviolet catastrophe, and Planck's revolutionary solution that birthed quantum theory. Discover the dual nature of light and matter through detailed analyses of the photoelectric effect, Compton scattering, and de Broglie's matter wave hypothesis, culminating in the famous double-slit experiment that demonstrates wave-particle duality. Master the mathematical framework of quantum mechanics by deriving Schrödinger's equation and understanding Born's probabilistic interpretation, wavefunction normalization, and expectation values. Investigate atomic structure through the Bohr model, spectral series, and laser physics principles including stimulated emission and Einstein coefficients. Delve into fundamental quantum mechanical problems including the free particle, particle in 1D/2D/3D boxes, step potentials, quantum tunneling, finite potential wells, and Dirac delta potentials. Conclude with the quantum harmonic oscillator using analytic methods to derive eigenvalues and eigenfunctions. Throughout the series, engage with problem-solving sessions designed for competitive examinations and explore advanced concepts like the uncertainty principle, Ehrenfest theorem, probability current, momentum space wavefunctions, and degeneracy in quantum systems.
