# Why is Planck's Constant important?

Jun 6, 2017

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,

${u}_{l a m \mathrm{da}} d \left(l a m \mathrm{da}\right) = \frac{8 \pi h c}{l} a m {\mathrm{da}}^{5} \cdot \frac{\mathrm{dl} a m \mathrm{da}}{{e}^{\frac{h c}{l a m \mathrm{da} k T}} - 1}$

Where one quantum of radiation would have an energy, $E = \frac{h c}{l a m \mathrm{da}}$, 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 $\frac{h}{2 \pi}$).

Examples would include,

1) de Broglie relation -
$l a m \mathrm{da} = \frac{h}{p}$

2) Schrodinger equation -

$\frac{i h}{2 \pi} \frac{\partial \psi}{\partial t} = - \frac{{h}^{2}}{8 {\pi}^{2} m} {\left(\nabla\right)}^{2} \psi + V \left(\vec{r} , t\right) \psi$

3) Commutator of $x$ and ${p}_{x}$ -

$\left[x , {p}_{x}\right] = \frac{i h}{2 \pi}$

And so on.

It is to quantum mechanics, what the constants ${\epsilon}_{0}$ and ${\mu}_{0}$ are to Electricity and Magnetism.