Lect37_[Compatibility_Mode] (1)

Lect37_[Compatibility_Mode] (1) - Physics 344 Foundations...

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Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir Applications Their Applications Instructor: Dr. Mark Haugan Office: PHYS 282 haugan@purdue.edu TA: Dan Hartzler Office: PHYS 7 dhartzle@purdue.edu Grader: Shuo Liu Office: PHYS 283 liu305@purdue.edu Office Hours: If you have questions, just email us to make an ppointment. e enjoy talking about physics! appointment. We enjoy talking about physics! Reading: Six Ideas Unit Q, Chapters 6, 7, 8, 10 and 11 Notices: Final Exam Tuesday, December 14 7:00pm in MSEE B012
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3-D Quantum Systems We will wrap up this semester with a brief look at the structure of atoms and nuclei as discussed in chapters 9, 12 and 13 in the text. To prepare, we first analyze a couple of simpler 3-d systems. The first consists of an electron trapped in a type of crystal defect called a olor center. color center. We consider the case of ionic crystals called alkali halides, like lithium fluoride or ordinary salt – sodium chloride. These consist of alternating positive and negative ions. Recall that typical atom size makes d 2.3 x 10 -10 m. + + + + + - -- - - Perfect crystals are transparent and colorless, but when exposed to radiation become colored. This is a consequence of one type f damage that the radiation does to the + + + + + + + + - of damage that the radiation does to the crystal.
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Color Centers in Ionic Crystals: Electrons in 3-d Boxes The box on the far left is meant to indicate a location from which a negative ion is missing. Obviously, an electron could become bound within such a region because, like the missing ion, an electron is negatively charged. Light absorbed and emitted in transitions between the energy eigenstates of the electron-crystal system in which electrons are bound in the larger R-type defects turn out to be responsible for the colors of radiation damaged crystals. The idea of modeling an electron bound within an F- or an R-type defect as an electron in a rectangular box of appropriate shape and size is pretty natural and it turns out that such simple models account quite nicely for what is observed.
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The energy eigenstates of an electron bound in such a defect satisfy the 22 2 2 222 (, ,) (, ,) (, ,) E xyz xyz Vxyz xyz x y z ψψ ψ ⎛⎞ ∂∂∂ =− + + + ⎜⎟ ∂∂ = time-independent Schrödinger equation, which in 3-d has the form 2 mx ⎝⎠ where V(x,y,z) represents the interaction of the electron with ions surrounding the defect. e’ve seen that finding normalizable solutions of this fundamental equation of We ve seen that finding normalizable solutions of this fundamental equation of quantum mechanics determines both the energies of the states the system can exist in and the corresponding energy eigenfunctions that determine where we are likely to detect the electron within the detect when it is in the corresponding energy eigenstate.
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This note was uploaded on 03/23/2011 for the course PHYS 344 taught by Professor Garfinkel during the Fall '08 term at Purdue University-West Lafayette.

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Lect37_[Compatibility_Mode] (1) - Physics 344 Foundations...

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