【正文】 ON THE ROAD AGAIN… Final Destination – Quantum Mechanics Taking the Trip From Classical Physics to Quantum Mechanics What is Quantum Mechanics one may ask? Well, in a nutshell, quantum mechanics is: – The FUNdamental branch of physics replacing classical Newtonian Mechanics and Electromagism at the atomic and subatomic levels. – Quantum mechanics provides explanations for many phenomena that are unattainable through classical mechanics ? Namely : quantization, wave – particle duality, the uncertainty principle, quantum entanglement Don?t be fooled, this will be no short trip… ? Quantum theory ideas did not originate overnight. There were numerous experiments and observed phenomena that eventually led to this modern way of thought. ? The move from General Relativity to Quantum mechanics is a huge step, since the two theories seemingly contradict each other. The two fundamental issues yielding this contradiction are。 – Classical is essentially a deterministic approach while quantum mechanics is essentially indeterministic – General relativity relies mainly on gravity while quantum mechanics relies on three fundamental forces, the strong, weak, and electromagic. ? (though these forces are imperative in Quantum Theory, we will leave out a discussion of them here, for they will be covered in a latter presentation) For the remainder.. We will look at the major players on the road to the discovery and development of this way of thought.) Why are we going here? Two fundamental discrepancies between experimental observations and classical physics were noticed in the late 1800?s. These two discrepancies (namely – the ultra violet catastrophe and the discrete spectral line phenomena) caused scientist to reexamine several established ideas and arrive at a new way of thought. EVERYONE JUMP IN THE VAN! We?re hittin the road! ? Problem 1 : Energy and Blackbody radiation ? Intro。 – A black body is a surface which absorbs all radiation and at a given temperature T, can also emit radiation – Thus, using the ρ(λ,T) energy function, holding T constant, the individual wavelengths λ of the radiation can be analyzed – At the turn of the 20th century, this in fact was done and the observations were first recorded by Otto Lummer and Ernst Pringsheim and then again the following year by Heinrich Rubens and Ferdinand Kurlbaum ? The results gathered are shown in the following figure Results Uh Oh! ? According to the Equipartition Theorem (a nonquantum theorem) every degree of freedom of a system must share equally in the energy available to the system, – Take for example, a blackbody radiation of dimension l , then we know that wavelengths are given by λ = (2l )/ n, where n = 1,2,3 …. – Each of these represent a degree of freedom, and therefore, by the equipartition theorem, should share the energy equally. – Thus, since there are infinitely many waves as the wavelength gets shorter, it would be assumed that the majority of the light (ie radiation) would be at the short wavelength end of the spectrum, as shown by the dotted line。 ? Notice the dotted line… Why is this a problem? Lets do the math… ? A major problem arises, since we know from derivations that follow directly from the equipartition theorem, done by Rayleigh and Sir James Jeans, that through classical analysis, the energy density function can be expressed as: where k is Boltzmann?s constant ? But it is easily seen that by applying basic calculus the limit of as λ approaches 0, is infinity. Obviously contradicting the observed results shown in the figure by the solid line. If this were indeed the case, the results would be described by the dotted line in the previous figure. ? This discrepancy and “blow – up” at short wavelengths is often referred to as the “ultraviolet catastrophe” and spurred much thought as to how to remedy it. FLAT TIRE!! Our classic car is getting old, time to trade it in ? The discrepancy between the observational results and this equation is an intense problem. Since the energy density equation derived by Jeans in 1905, followed directly from the well established equipartition theorem, which was a consequence of general relatively. Thus because these do not correlate, it implies that the overlying theory must be inadequate. Problem 1 –Flat Tire now we have Problem 2 – running out of gas ? The second phenomena leading to quantum theory stems from the pattern of spectral lines emitted by an element – When an electric arc passes through a sample of gas, it is observed that only certain frequencies of light are present. – When observing the spectral lines by separating them with a prism, it is observed that the wavelengths are distinct to the element emitting the spectrum What?s so bad about that? ? This observation directly contradicts the predictions of classical physics – According to classical physics, accelerated particles must emit electromagic radiation, and