Question

Why is Planck's Constant important?

Answer 1

Planck's constant is instrumental and an unavoidable constant which appears in quantum mechanics.

Explanation:

Even though it was first introduced in the Planck's law,

`u_(lamda)d(lamda) = (8pihc)/lamda^5*(dlamda)/(e^((hc)/(lamdakT))-1)`

Where one quantum of radiation would have an energy, `E = (hc)/(lamda)`, the concept of quantized radiation was extended by Einstein, later by Bohr in their theories as a part of the old quantum theory.

Today almost all important relationships in quantum mechanics, contain Planck's constant (or the reduced Planck's constant `h/(2pi)`).

Examples would include,

1) de Broglie relation -
`lamda = h/p`

2) Schrodinger equation -

`(ih)/(2pi)(delpsi)/(delt) = -(h^2)/(8pi^2m)(nabla)^2psi + V(vec r,t)psi`

3) Commutator of `x` and `p_x` -

`[x,p_x] = (ih)/(2pi)`

And so on.

It is to quantum mechanics, what the constants `epsilon_0` and `mu_0` are to Electricity and Magnetism.