LectureQ7

LectureQ7 - Chapter 7 In chapter 6 we learned about a set...

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4/19/2004 H133 Spring 2004 1 Chapter 7 In chapter 6 we learned about a set of rules for quantum mechanics. Now we want to apply them to various cases and see what they predict for the behavior of quanta under different conditions. ± Free Particle: We already looked at a special case of this for the 2-slit experiment where the free particle was in an eigenstate of momentum…it had a well defined momentum and therefore wavelength. ± Bound Particle: Many particles in nature are not free but bound in a system. ² Electron in an atom. ² Proton in a nucleus ² Atom in a lattice. Bound Systems are perhaps the most interesting cases for us to consider. We see much of the interesting features of quantum mechanics. ± However, bound systems can be very complicated (even for advanced physics courses!) ² Uranium Atom…no way of solving that in an exact way…in fact you get much beyond helium and it gets very hard. ± We will make a number of simplifying assumptions (approximations). Although these are approximations do not significantly alter our results…all the interesting features of quantum mechanics will still be there.
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4/19/2004 H133 Spring 2004 2 Bound System Typically if a particle is bound it is because there is a force from other near by particles. ± e.g. electron bound to a proton in the hydrogen atom. ± In many cases one of the particles (electron) is much less massive that the particles that are holding it near by (proton.) ² In this case, the motion of the less massive particle does not significantly effect the motion of the more massive particle(s). ² We can think of the less massive particle as being in a potential energy field (“well”) of the more massive particles…and forget about the more massive particles. We will start with examples that are simpler than the hydrogen atom (we’ll get back to that later). ± Start with one-dimensional potential r ke r V 2 ) ( = r E V(x) Classically Allow Region x Classically Forbidden Region Classically Forbidden Region Turning Point K
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4/19/2004 H133 Spring 2004 3 Energy Eigenfunctions
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This note was uploaded on 06/03/2011 for the course H 133 taught by Professor Furnstahl during the Spring '11 term at Ohio State.

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LectureQ7 - Chapter 7 In chapter 6 we learned about a set...

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