Why is Planck's Constant important?

1 Answer
Jun 6, 2017

Answer:

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.