Considering the Death Star's ruinous design flaw, it's hardly surprising that the Empire developed a rather inefficient way to blow up planets. According to astrophysicist Ethan Siegel, the massive-green-energy-beam approach might look cool, but to get the job done right, you need something else.
That would be antimatter.
Writing at his blog, Starts With A Bang!, Siegel observes that the amount of energy required to demolish Alderaan (2.24 × 10^32 Joules) would, by means of simple heat diffusion, melt all the equipment around it. And, firing that much energy in a specific direction should have caused a massive recoil. Either that recoil was edited out of the "historical footage" of the Death Star's attack, or some elaborate technology, consuming vast amounts of additional power, would be necessary to keep the massive space station from zipping backwards like a moon-sized billiard ball.
However, a mere 1.24 trillion tonnes of antimatter (the mass of a small asteroid) would have been sufficient to destroy Princess Leia's adopted home world. The hard part would be storing that much antimatter in a Death Star-sized object. But here's the thing: just like matter binds to itself through the electromagnetic force and — if you get a large amount of "stuff" together — through gravitation, antimatter behaves exactly in the same way.
As Siegel explains:
We've been able to create neutral antimatter and store it, successfully, for reasonably long periods of time: not mere picoseconds, microseconds or even milliseconds, but long enough that it's only our failure to keep normal matter away from it that causes it to annihilate in short order.
It isn't unreasonable that an advanced technological civilization — one that's mastered hyperdrive and faster-than-light travel — could harness, say, the energy from an uninhabited star and use it to produce neutral antimatter. The way we do it on Earth in particle accelerators is relatively simple: we collide protons with other protons at high energies, producing three protons and one antiproton as a result. That antiproton could then be merged with a positron to produce neutral antihydrogen. You might wish for rocky, crystalline structures based on elements like silicon or carbon, but under the right conditions, hydrogen can produce a crystal-like structure.
In the interiors of gas giants like Jupiter and Saturn, the incredibly thick hydrogen atmosphere extends down for tens of thousands of kilometers. Whereas the pressure at Earth's atmosphere is around 100,000 Pascals (where a Pascal is a N/m^2), at pressures of tens of Gigapascals (or 10^10 Pascals), hydrogen can enter a metallic phase, something that should no doubt happen in the interiors of gas giant planets.
If we could achieve this state of matter, hydrogen would actually become an electrical conductor, and is thought to be responsible for the intense magnetic field of Jupiter. All the laws of physics suggest that if this is how matter behaves, and we can do this with hydrogen, then this must also be how antimatter — and hence, antihydrogen — behaves, too.
So all it would take, if you want to destroy an (Earth-like) planet like Alderaan, is a little over a trillion tonnes of metallic antihydrogen, and to transport it down to the planet's surface. Once it hits the planet's surface, it should have no trouble clearing a path down near the core, where the densities are highest.
See? That's not so hard.