01 - Physics 6210/Spring 2007/Lecture 1 Lecture 1 Relevant...

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Unformatted text preview: Physics 6210/Spring 2007/Lecture 1 Lecture 1 Relevant sections in text: § 1.1 What is a theory? Students often consider quantum mechanics to be rather strange compared to other theories they have encountered ( e.g., classical mechanics, electromagnetic theory). And I guess it is a little unsettling to find position and momentum being represented as dif- ferential operators, particles being described by complex waves, dynamics being defined by the Schr¨ odinger equation, measurements characterized by probabilities, and so forth. In particular, the rules of quantum mechanics, at first sight, seem rather strange com- pared to the rules of Newtonian mechanics (essentially just Newton’s 3 laws). But a lot of the intuitive appeal of Newton’s laws comes from years of familiarity. Unfortunately, the “strangeness” of quantum mechanics, largely bred from lack of familiarity, often leads to the feeling that the subject is very difficult. Of course, the subject is not easy; nor should it be - it is one our most advanced descriptions of nature! But even if the basics seem a little difficult, it is only because one is having to use new mathematical models for familiar physical structures. After all, wasn’t it a little unsettling when you first started using vectors in a systematic way to describe displacements, velocities, and so forth? (Can you remember that far back?) So, I would like to begin by emphasizing that, in many ways, quantum mechanics is a theory like any other. To do this I must give a very coarse grained description of what a theory is in general, and quantum mechanics in particular. Of course, the devil – and the physics – is in the details. Essentially, a physical theory is a set of rules ( i.e., postulates) that can be used to “explain” and/or predict the behavior of the world around us – in particular, the outcome of experiments. Which experiments can be explained, how to characterize the physical ingredients in these experiments, what information needs to be specified in advance, etc. are part of the rules of the theory. By the way, keep in mind that a theory can never be said to be “true”, but only that it “agrees with experiment”. It is always possible that the next experiment will falsify the theory. And it is possible that more than one theory will be able to explain a given set of results. Insofar as these results are all we have experimental access to, the theories are equally good. Usually, though, there is one theory that explains the most results with the “simplest” postulates. This theory is usually considered the best. So, while classical mechanics can be used to explain a wide variety of macroscopic observations, quantum mechanics can also explain these results and a host of other results from microscopic physics (atomic physics, nuclear physics, etc. ) that cannot readily be explained using classical mechanics....
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01 - Physics 6210/Spring 2007/Lecture 1 Lecture 1 Relevant...

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