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Quantum Theory But if an electron acts as a wave when it is moving, WHAT IS WAVING? When light acts as a wave when it is moving, we have identified the ELECTROMAGNETIC FIELD as waving. But try to recall: what is the electric field? Can we directly measure it? Quantum Theory Recall that by definition, E = F/q. We can only determine that a field exists by measuring an electric force! We have become so used to working with the electric and magnetic fields, that we tend to take their existence for granted. They certainly are a useful construct even if they don’t exist. Quantum Theory We have four LAWS governing the electric and magnetic fields that as a group are called: MAXWELL’S EQUATIONS (Gauss’ Law for electric fields which is equivalent to Coulomb’s Law; Gauss’ Law for magnetic fields, Ampere’s Law which is equivalent to the magnetic force law, and Faraday’s Law). By combining these laws we can get a WAVE EQUATION for EM fields, and from this wave equation we can get the speed of the EM wave and even more (such as reflection coefficients, etc.). Quantum Theory But what do we do for electron waves? What laws or new law can we find that will work for matter to give us the wealth of predictive power that MAXWELL’S EQUATIONS have given us for light? Quantum Theory The way you get a law is to try to explain something you already know about, and then see if you can generalize. A successful law will explain what you already know about, and predict things to look for that you may not know about. This is where the validity (or at least usefulness) of the law can be confirmed. Quantum Theory Schrodinger started with the idea of Conservation of Energy: KE + PE = Etotal . He noted that there are two relations between the particle and wave ideas: E=hf and p=h/ ? , and both could be related to energy: KE = (1/2)mv2 = p2/2m, and that ?=h/p, so that p = h/? = (h/2?)*(2?/?) = ?k = p, so KE = ?2k2/2m Etotal = hf = (h/2?)*(2?f) = ??. Quantum Theory He the