Quantum numbers are fundamental, discrete properties that characterize particles and arise from the symmetries of quantum systems. They include the principal quantum number, which specifies an electron's energy level or shell in an atom, and the orbital angular momentum quantum number, which describes the shape of the orbital within that shell. Additionally, the magnetic quantum number defines the orientation of the orbital in space, while the spin quantum number represents the intrinsic spin of a particle. Related to spin, the magnetic spin quantum number describes the specific orientation of this intrinsic spin in a magnetic field. Moving beyond electron structure, the isospin quantum number and its projection are used to describe nucleons in the context of the strong nuclear force, providing a symmetry between protons and neutrons. Other quantum numbers reflect the presence of specific quark flavors within particles, such as strangeness, charm, bottomness, and topness. Particles are also assigned a baryon number if they are baryons (like protons or neutrons) and a lepton number if they are leptons (like electrons or neutrinos).
Further quantum numbers include parity, which describes how a particle behaves under spatial inversion, and charge conjugation, which indicates its transformation properties under particle-antiparticle exchange. G-parity combines charge conjugation with isospin rotation for mesons, while hypercharge, defined as the sum of baryon number and strangeness, plays a role in strong interactions. Finally, total angular momentum combines orbital and spin angular momentum, and weak isospin relates to weak force interactions. These quantum numbers are crucial for identifying and classifying particles as well as determining the possible interactions they can undergo, as they are often conserved in processes.
Beyond these quantum numbers, particles also exhibit other properties that are not quantized or conserved in the same way but are still essential for understanding quantum behavior. The wavefunction encapsulates information about the probability amplitude of a particle’s state, while phase represents relative differences that affect interference patterns in quantum systems. Coherence is another critical property, indicating the correlation between quantum states' phases and enabling phenomena like superposition and entanglement. Entanglement itself describes a deep, non-local connection between particles, where the state of one particle depends on another, yet this relationship is not a quantum number. Particles with spin also have a spin orientation in space that affects interactions but is not captured by the spin quantum number alone.
Certain properties, like parity violation in weak interactions, describe how symmetries might be broken in processes without implying a specific conserved value. Chirality and helicity further describe handedness and the alignment of spin with momentum, respectively, particularly relevant for massless particles, though they are not quantum numbers. Other important particle attributes include mass and energy, which are fundamental but continuous variables. Decay modes and lifetimes characterize particle stability and transformation but do not represent discrete quantum values. Properties like cross-sections and scattering amplitudes measure interaction probabilities, while gauge symmetries and coupling constants, which define interaction strengths, set up interaction frameworks rather than particle-specific quantum states. Collectively, these properties play crucial roles in quantum behavior and interaction dynamics but remain distinct from quantum numbers in their non-discrete or environment-dependent nature.