QUANTUM MECHANICS

 Why do we need quantum mechanics?

Quite simply - you need quantum mechanics because - past a certain point - classical mechanics just doesn’t work.

Classical electromagnetism and thermodynamics was able to prove that when things get hot - they glow.

You’ve all seen this:

As physicists - the next job was to work out how much it is glowing - and at what frequencies? How does this change with temperature?

So, Rayleigh and Jeans came up with a law which said that the spectral radiance (the amount of light emitted at each wavelength) of an object is given by:

Bλ(T)=2ckbTλ4${�}_{�}(�)=\frac{2�{�}_{�}�}{{�}^4}$

Where λ$�$is the wavelength of the light.

Now - as far as classical physics is concerned, this is absolutely the correct answer to have derived.

But.

What happens when λ$�$ gets small?

Bugger.

Yeah - the theory predicts that the intensity goes off to infinity, as the wavelength goes to zero (the purple/blue line on the diagram).

That would imply that every single object in the universe was constantly spewing deadly X-rays everywhere - all of the time.

This isn’t what happens.

The observed spectrum is the green line - it goes up from zero, peaks, and goes back down. At no point does it shoot off to infinity and bathe the universe with deadly radiation!

---

This problem stumped a lot of people for a long time - it even had a badass name: “the Ultraviolet Catastrophe”.

To get around this problem, Max Planck postulated that light came in discrete “bundles” - or “quanta”, which had energy E$�$ proportional to their frequency:

E=hν=hcλ$�=ℎ�=\frac{ℎ�}{�}$

For a bunch of complicated maths reasons (statistical physics is the easiest way to prove this), this added postulate leads to Planck’s law:

Bλ(T)=2hc2λ51ehcλkbT−1${�}_{�}(�)={\displaystyle \frac{2ℎ{�}^2}{{�}^5}\frac{1}{{�}^{\frac{ℎ�}{�{�}_{�}�}}-1}}$

Which does accurately predict the correct intensities observed:

So that’s why you need it - because our description of nature doesn’t work without it.

Trust me - if physics knew of a decent way to do away with the restrictions that quantum mechanics places on us, then we sure as hell would.

But nobody has found a better theory in 100 years - they just find better and better refinements of our old one.

Quantum mechanics is needed because the universe appears to behave in a quantum fashion - simple as that.