Harmonic Potential: Schrödinger Equation and Eigenstates

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Page 3 of 4

Covers harmonic oscillations, energy eigenstates, and the stationary Schrödinger equation in wave mechanics.

Explores the probability distribution in the canonical ensemble and the Boltzmann distribution.

Explores max entropy, Shannon's entropy, Lagrange multipliers, and Monte Carlo sampling techniques.

Explores wave functions, quantum numbers, and orbital shapes in the electronic structure of atoms.

Explores the solutions to the Schrödinger Equation in Quantum Chemistry, emphasizing wavefunction properties and energy quantization.

Covers creation and annihilation operators in quantum mechanics and their applications in harmonic oscillators.

Explores the Ehrenfest Theorem, connecting quantum and classical mechanics through expectation values and harmonic oscillator dynamics.

Explores Gaussian mixture models and denoising noisy signals using a probabilistic approach.

Introduces random variables, probability distributions, and expected values through practical examples.

Explores angular wave functions, electron orbitals, and quantum numbers in hydrogen atoms.