Wave–particle duality is the quantum concept that every elementary particle or quantum entity exhibits both wave‑like and particle‑like behavior. For example, electrons can produce interference patterns in a double‑slit experiment (a wave property), yet also arrive at a detector in discrete packets of energy (a particle property). This duality is fundamental to quantum mechanics and tells us that classical categories of “wave” and “particle” are merely limiting approximations.

The Heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision at the same time. More precisely, the product of the uncertainties in position (Δx) and momentum (Δp) is at least on the order of Planck’s constant (ℏ/2). This principle isn’t due to measurement flaws but reflects a fundamental limit on how precisely nature allows those properties to be defined simultaneously

Quantum superposition is the principle that a quantum system can exist in multiple, classically mutually exclusive states at once—until it is measured. For instance, a single electron in an atom can simultaneously occupy two different orbitals in the mathematical description. Only upon measurement does the system “collapse” to one of the possible states, with probabilities given by the squared amplitudes of the wavefunction.

Quantum entanglement is a phenomenon in which two or more particles become linked so that the state of one instantly influences the state of the other, no matter how far apart they are. When entangled, measuring a property (like spin) of particle A immediately determines the corresponding property of particle B. Entanglement defies classical intuition about locality and underpins applications such as quantum teleportation and quantum key distribution.

Quantum tunneling is the effect whereby a particle can pass through a potential energy barrier even if its energy is classically insufficient to overcome it. Thanks to the probabilistic spread of the particle’s wavefunction, there is a nonzero probability that it will “tunnel” through and appear on the other side. Tunneling is crucial in nuclear fusion in stars, as well as in modern electronics like tunnel diodes and the scanning tunneling microscope.

The Schrödinger equation is the fundamental wave equation of non‑relativistic quantum mechanics, governing how a system’s wavefunction evolves over time. In its time‑dependent form, it relates the Hamiltonian operator (total energy) acting on the wavefunction to its time derivative. Solving the Schrödinger equation for a given potential yields quantized energy levels and probability distributions for measurable properties.

Quantum decoherence is the process by which a system loses its coherent quantum behavior—such as superposition—through interaction with its environment. As the system becomes entangled with outside degrees of freedom, its phase relationships are scrambled, effectively turning pure quantum states into classical mixtures. Decoherence explains why macroscopic objects appear classical and poses a major challenge for building large‑scale quantum computers.

The Pauli exclusion principle states that no two identical fermions (particles with half‑integer spin, like electrons) may occupy the same quantum state simultaneously. This rule arises from the antisymmetric nature of the fermionic wavefunction and underlies the electronic structure of atoms, the stability of matter, and the diversity of chemical behavior: it forces electrons to fill distinct orbitals in an atom.

A qubit, or quantum bit, is the basic unit of quantum information, analogous to a classical bit but capable of existing in any superposition of its two basis states |0⟩ and |1⟩. Unlike a classical bit (strictly 0 or 1), a qubit’s amplitudes can encode complex probability amplitudes, enabling phenomena like quantum parallelism and entanglement that lend quantum computers their potential advantage for certain tasks.