Historical Development: Quantum mechanics emerged in the early 20th century to explain phenomena that classical physics couldn’t account for, including blackbody radiation (Planck), the photoelectric effect (Einstein), and atomic spectra (Bohr).
Key Experimental Foundations:Hilbert Space: Quantum states are represented as vectors in a complex Hilbert space. The state vector |ψ⟩ contains all information about the system.
Operators: Physical observables are represented by Hermitian operators. The eigenvalues of these operators correspond to the possible measurement outcomes, and the eigenvectors represent the states after measurement.
Schrödinger Equation: The time evolution of quantum systems is governed by the Schrödinger equation: iħ∂|ψ⟩/∂t = H|ψ⟩, where H is the Hamiltonian operator representing the total energy.
- Wave-Particle Duality: Light and matter exhibit both wave-like and particle-like properties (de Broglie wavelength λ = h/p)
- – Uncertainty Principle: Fundamental limits on precision of complementary measurements (ΔxΔp ≥ ħ/2)
- – Quantization: Physical quantities like energy and angular momentum come in discrete amounts