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Unformatted text preview: M. S. Shell 2008 1/22 last modified 9/23/2010 How the microscopic world works ChE210A In order to conceptualize the molecular origins of thermodynamic equilibrium, it is important to first understand the fundamental principles by which molecules interact. Moreover, as science and technology increasingly elucidate and rely upon nanoscale phenomena, molecular driving forces are a critical piece of any technical education. Quantum theory So, how does the world really work? What are the most fundamental, basic principles that form the basis of reality as we know it? Currently our understanding of reality rests upon two principle fields in physics: quantum theory and relativity. Both of these theories have been the subject of stringent experimental tests over the past century. Perhaps surprisingly, there are some incompatibilities between quantum theory and relativity, which are driving the develop- ment of new fundamental physical theories, such as the string theory. Luckily, clashes between these two bodies of physics manifest only under rare circumstances; moreover, relativistic effects are not often directly relevant to most everyday problems and to the kinds of problems studied in chemical thermodynamics. So we can safely begin our discussion at the level of quantum theory. Quantum mechanics describes the complete time-evolution of any system. It is most easily described by imagining a system of fundamental particles, like electrons or protons. Each particle has associated with it a position variable, g G ,g , , etc., where each g is a vector quanti- ty , , . Then, the complete state of the system at any point in time is specified by a func- tion g G , g , , called the wavefunction . The wavefunction takes on complex values, of the form . The physical significance of the wavefunction is that its norm, g G ,g , , g G , g , , , gives the joint probability that particle one is at g G , particle 2 is at g , etc, at the time . Here denotes the complex conju- gate, i.e., . The quantity therefore is always real and positive, . The central focus of quantum mechanics is the complex-valued wavefunction , whose interpretation is that gives the probability the system is at a specific microscopic state at a given time. The wavefunction describes the evolution of probabilities . This is very different from Newto- nian mechanics, in which each particle has an exact position at time , and not a possible distribution of positions. Quantum mechanics says that this distribution is the most we can M. S. Shell 2008 2/22 last modified 9/23/2010 possibly know about the system; we cannot predict the position of the particles to more accuracy. There is some inherent randomness in nature, and the best that we can do is under- stand the probabilities of different possible outcomes. This may sound a bit strange because we are not used to this kind of behavior at the macroscopic scale. we are not used to this kind of behavior at the macroscopic scale....
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