Why is Planck's Constant important?

Question

Why is Planck's Constant important?

1 Answer

Impact of this question

6206 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-06T09:08:07

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,

$u_{λ} d (λ) = \frac{8 π h c}{λ^{5}} \cdot \frac{d λ}{e^{\frac{h c}{λ k T}} - 1}$ $u_(lamda)d(lamda) = (8pihc)/lamda^5*(dlamda)/(e^((hc)/(lamdakT))-1)$

Where one quantum of radiation would have an energy, $E = \frac{h c}{λ}$ $E = (hc)/(lamda)$ , 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 $\frac{h}{2 π}$ $h/(2pi)$ ).

Examples would include,

1) de Broglie relation -
$λ = \frac{h}{p}$ $lamda = h/p$

2) Schrodinger equation -

$\frac{i h}{2 π} \frac{\partial ψ}{\partial t} = - \frac{h^{2}}{8 π^{2} m} {(\nabla)}^{2} ψ + V (\to r, t) ψ$ $(ih)/(2pi)(delpsi)/(delt) = -(h^2)/(8pi^2m)(nabla)^2psi + V(vec r,t)psi$

3) Commutator of $x$ $x$ and $p_{x}$ $p_x$ -

$[x, p_{x}] = \frac{i h}{2 π}$ $[x,p_x] = (ih)/(2pi)$

And so on.

It is to quantum mechanics, what the constants $ε_{0}$ $epsilon_0$ and $μ_{0}$ $mu_0$ are to Electricity and Magnetism.

Science

Math

Humanities

... and beyond

Why is Planck's Constant important?

1 Answer

Explanation:

Related questions

Impact of this question