Below i am describing about Dirac equation by collecting information through wikipedia and BBC. Hope that will be impressively helpful to you why it is actually powerful equation in the science world.
Definition of Dirac Equation:
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1⁄2 massive particles such as electrons and quarks, for which parity is a symmetry, and is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It accounted for the fine details of the hydrogen spectrum in a completely rigorous way.
Original Dirac Equation:
Where is the wave function for the electron of rest mass m with spacetime coordinates x, t. The p1, p2, p3 are the components of the momentum, understood to be themomentum operator in the Schrödinger equation. Also, c is the speed of light, and ħ is the Planck constant divided by 2π. These fundamental physical constants reflect special relativity and quantum mechanics, respectively.
Why Dirac Equation is Powerful?
One mathematical statement unites the two foundations of present day material science: quantum mechanics and relativity.
This mathematical statement is intense, mostly as a result of what it implies and the part it played ever century material science. The mathematical statement was found in the late 1920s by physicist Paul Dirac. It remains exceptionally powerful.
It united two of the most vital thoughts in science: quantum mechanics, which depicts the conduct of minor articles; and Einstein’s unique hypothesis of relativity, which portrays the conduct of quick moving items. Accordingly, Dirac’s mathematical statement depicts how particles like electrons carry on when they fly out near the velocity of light.
Physicist Jon Butterworth of University College London in the UK likewise picked the Dirac mathematical statement. Maybe most significantly, the Dirac mathematical statement anticipated the presence of antimatter – the mirror picture of every single known molecule. Antimatter was later found to exist in this present reality.