Why a light quanta has two units: h and h=2pi?

Answer 1

I think you are referring to Planck's constant (h) and Dirac's constant (h-bar), where:

h-bar = h/(2*pi)

You use h when you use frequency (Hertz), which is often denoted as the Greek letter nu. You use h-bar when you use angular frequency (radians per second), which is often denoted as the Greek letter omega. The relationship between frequency and angular frequency is:

omega = 2*pi*nu

Thus, when you use omega, you need to divide by 2*pi.

For example, consider the energy of a photon.

E = h-bar*omega = (h/(2*pi))*(2*pi*nu) = h*nu

As you can see, the two energies are the same.

So really your question comes down to why angular frequency is ever used. Well, an oscillator with frequency nu can be represented by a sinusoid like:

sin( 2*pi*nu*t )

That 2*pi gets cumbersome, especially when taking derivatives. So angular frequency is used instead, giving us:

sin( omega*t )

However, in order to use angular frequency, we have to remember to generate some new constants that divide by (2*pi).

Answer 2

because you can use it in diferent equations and its easier to normalize h than add 2*PI in every equation where h is inside a trigonometric funcion