The scale of physical phenomena governed by the principles of quantum mechanics.The quantum level is the scale at which the behavior of matter and energy is governed by the principles of quantum mechanics. This typically involves systems of atomic and subatomic dimensions, where quantities like energy, momentum, and angular momentum are quantized — they can only take on discrete values rather than a continuous range. At this scale, particles exhibit wave-like properties, and phenomena such as superposition and entanglement become central to describing physical reality.
The concept emerged in the early 20th century with Max Planck's quantization of energy in 1900 and Niels Bohr's model of the atom in 1913, later formalized by Werner Heisenberg, Erwin Schrödinger, and others in the mid-1920s.
At the quantum level, the state of a system is described by a wavefunction, which encodes probabilities for the outcomes of measurements. Observable quantities correspond to operators acting on this wavefunction, and the possible measurement outcomes are the eigenvalues of these operators. The evolution of the wavefunction is governed by the Schrödinger equation, which is deterministic, while the act of measurement introduces an apparent randomness through the collapse of the wavefunction.
The quantum level underpins technologies such as semiconductors, lasers, and magnetic resonance imaging, and is the foundation for emerging quantum computing and quantum cryptography.
At the quantum level, particles can pass through barriers they classically could not overcome, a phenomenon known as quantum tunneling, which is essential for nuclear fusion in stars.
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