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Quantum mechanics (quantum physics) is the fundamental theory describing how matter and light behave at atomic and subatomic scales, where classical physics becomes insufficient. It explains phenomena such as quantized (discrete) energy and other observables, waveâparticle duality, and inherent limits on prediction accuracy captured by the uncertainty principle. Although it can be applied to complex systems (e.g., molecules with many atoms), questions about measurement and interpretation can become philosophically challenging, especially when considering observers or even the universe as a whole. A central feature of quantum mechanics is its probabilistic predictions: a systemâs state is represented by a wave function, and measurement outcomes are determined using probability amplitudes via the Born rule. The wave function evolves deterministically in time according to the Schrödinger equation, governed by the Hamiltonian (the total energy operator). The theoryâs scope is broad: it provides mathematical formalisms for calculating properties of microscopic systems and underpins many modern fields and technologies, including quantum chemistry, quantum optics, quantum computing, and materials science.
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In quantum mechanics, a systemâs state is described by a wave function, which assigns a complex probability amplitude to each point in space (or to each basis state). The probability of obtaining a particular measurement outcome is not taken directly from the wave function itself, but from the Born rule: it is given by the square of the absolute value of the relevant complex amplitude (or, more generally, by expectation values/projection operators). This is why quantum mechanics predicts probabilities rather than certain results for quantities like position. The wave functionâs time evolution is governed by the Schrödinger equation, which deterministically updates the collection of probability amplitudes from one time to another. Because amplitudes are complex, they can interfere: different paths or components of the wave function can add or cancel, producing observable interference patterns. A key implication is that the same underlying wave function can yield different probability distributions depending on how measurements are arranged, as illustrated by interferometer and double-slit-type setups.
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