alxm said:The reason why [tex]\hbar[/tex] is set to 1 rather than [tex]h[/tex] is simply because you tend to use the former a lot more. (e.g. the momentum operator)
clem said:It just turns out that h/2pi appears in so many equations that hbar is a convenient constant. Then it turns out that 1 is even more convenient.
The use of Planck units, which are a system of natural units based on fundamental physical constants, is a way to simplify calculations and express physical quantities without the need for arbitrary units or conversion factors. In this system, the reduced Planck constant, h-bar (h/2π), is used instead of the regular Planck constant, h, because it is a more convenient and natural choice for the fundamental unit of action.
H-bar is a fundamental constant in quantum mechanics that relates the energy of a quantum state to its frequency. It is also related to the uncertainty principle, which states that the more precisely one knows the position of a particle, the less precisely one can know its momentum, and vice versa. H-bar is used to define the smallest possible unit of action, known as the Planck constant, which plays a crucial role in quantum mechanics.
In the system of Planck units, h-bar is used to define the Planck length and Planck time, which are the smallest possible units of length and time, respectively. The Planck length is defined as the distance at which quantum effects are significant, and the Planck time is the time it takes for light to travel this distance. Both of these units are based on the fundamental constants of h-bar, c (the speed of light), and G (the gravitational constant).
No, h-bar is not just a shorthand for h in Planck units. While they are mathematically related (h-bar = h/2π), they have different physical meanings. H-bar is used to define the fundamental unit of action, while h is used to define the fundamental unit of angular momentum. In the context of quantum mechanics, h-bar is considered a more natural and convenient choice for the fundamental unit of action.
Yes, h-bar can be derived from other fundamental physical constants, specifically h, c, and G. This derivation is known as the Planck-Einstein relation, which relates the energy of a photon to its frequency and the reduced Planck constant. Other fundamental constants, such as the mass of an electron and the elementary charge, can also be used to derive h-bar and other Planck units, showing their interconnectedness in the fundamental laws of physics.