The reduced Planck constant, denoted as ħ (pronounced "h-bar"), is indeed a convention used in quantum mechanics and other areas of physics. It is related to the Planck constant (h) by the equation ħ = h / (2π). The choice to use the reduced Planck constant instead of the Planck constant alone is mainly a matter of convenience and mathematical elegance.
While it is possible to express the Planck units using the standard Planck constant, it would not be as convenient or commonly used. The Planck units are a system of natural units that are derived from fundamental physical constants, including the Planck constant. These units are used to express quantities in a way that eliminates any dependence on specific measurement systems or human conventions.
The use of the reduced Planck constant (ħ) in the Planck units simplifies the mathematical expressions and makes them more compact. The presence of the factor of 2π in the denominator of the definition of ħ arises naturally in many physical equations, particularly those involving angular momentum and quantum mechanical wavefunctions. Using the reduced Planck constant allows for a more elegant representation of these equations.
In summary, while it is technically possible to express the Planck units using the standard Planck constant, the use of the reduced Planck constant (ħ) is more convenient and commonly adopted due to its mathematical and conceptual advantages in quantum mechanics and related fields.