Why is Planck’s constant important in quantum mechanics?

Planck’s constant ($h$) is a fundamental physical constant that serves as the cornerstone of quantum mechanics, the field describing the behavior of matter and energy at the atomic scale. Its importance stems from several key roles:1

• Quantization of Energy: Introduced by Max Planck in 1900, the constant reveals that energy is not continuous but is emitted, transmitted, and absorbed in discrete packets called quanta. The energy ($E$) of a quantum is directly proportional to the radiation's frequency ($\nu$), expressed as $E=h\nu$.12
• Defining the Microphysical World: Because $h$ has a small but finite value, it dictates that the atomic world cannot be described by classical mechanics. It acts as the elementary quantum of action.12
• The Uncertainty Principle: The constant is central to the uncertainty principle, which states that the product of uncertainties in conjugate variables—such as position and momentum—must be at least $h/(4\pi )$. This reflects the fundamental wave-particle duality of nature.3
• Angular Momentum: A modified version, the reduced Planck’s constant ($\hslash =h/2\pi$), defines the quantization of angular momentum for particles like electrons bound to an atomic nucleus.1