The editors of Physics World (a quality mag) have published the results of a readers' survey of their favourite equations. Top of the list are the Maxwell equations (I can go with that), along with Euler's Equation.
Euler's Equation is beautiful, but is it Physics?
Then comes Newton's 2nd law (which isn't F=ma, it is F=dp/dt).
Followed by pythagorous (what is that doing there?)
Then the Schödinger equation, (okay), and finally E=mc2.
Whilst I can go with Maxwell, Newton (in the form of F=dp/dt) and Schrödinger, I take issue with the rest. Including E=mc2 as it is too clichéd. Euler should not be there as it isn't physicsy enough - it would be number one in a list of all time beautiful bits of maths. Similarly, pythagorus is nice, but it doesn't 'feel' right in this list for me.
What would I replace them with?
I'd replace E=mc2 with E2=m02c4+p2c2, as this reduces to E=m0c2 when p=0 and E=pc when m0=0 (e.g. for a photon, or in high energy situations and m0 is negligable.
I'd also have the de Broglie equation ('g' is pronounced as 'y'), p=h/λ. This is a phenomenal result, its generality was pure speculation, but speculation that turned out to be pretty good. (λ should come out as the greek letter 'lambda').
My third replacement? Oh, all right, Euler can stay. You've twisted my arm.
One of the nicest bits of physics, not really an equation, is the prediction and subsequent discovery of the Ω- (Omega-minus), also the discoveries of the neutrino and meson. One of the nicest experiments is muon time dilation. Okay, I'm a particle physics type... does it show? In addition, I do have a soft spot for the Meissner effect. Also, the nicest pieces of classical mechanics I can think of are a pingpong ball in a smooth stream of air and a gyroscope, suspended at one end with its axis horizontal.
I'd be interested to hear any comments upon my choices, or other candidates which I've missed.