Lecture35 - Physics 344 Foundations of 21st Century...

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Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 haugan@purdue.edu TA: Dan Hartzler Office: PHYS 7 dhartzle@purdue.edu Grader: Fan Chen Office: PHYS 222 chen926@purdue.edu Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! Help Session: Thursdays 2:00 – 4:00 in PHYS 154 Reading: Chapters 7, 10 and 11 in the text. Exam 2: THIS Thursday, December 1 at 8:00pm in ARMS B061
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An Electron in a Vertical Metal Film This idealized model offers us the opportunity to examine semi-quantitatively energy eigenvectors of another quantum system. In this case, the system of consists of the electron, the metal film and the Earth. The potential energy function for the system’s time-independent Schrödinger equation is the sum of the potential energy representing the electron’s interaction with the film and the linear potential energy function representing the electron’s gravitational interaction with the Earth. In the accompanying diagram the x now represents vertical position. Adding a horizontal line to the energy diagram for a suitable energy E demonstrates that states of this system with the electron bound in the film are possible. Note the classical turning points. V(x) x E -W x=a Knowing what we now know about the character of energy eigenstates of such systems and about the relationship between “local wavelength” and electron kinetic energy, let’s try to sketch what this system’s energy eigenvectors should look like.
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Let’s see how we did. We can use our numerical method to estimate both energy eigenvectors and the corresponding energy eigenvalues for this system. This excited state example clearly illustrates the correlation we commented on last lecture between eigenstate amplitude and local wavelength as a function of position. Longer local wavelength indicates lower electron kinetic energy in regions where the potential energy function is less negative. Classically, lower kinetic energy corresponds to slower electron motion. The larger amplitude of energy eigenstates in regions where the electron kinetic energy is the quantum version of this result. Lower speed passing through a region suggests that the particle is relatively more likely to be detected there, and this is just what the larger eigenstate amplitude in such regions implies.
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The Bouncing Neutron Experiment [Nature, 415 , 297 (2002)] As it happens there are solid materials from which free neutrons reflect and others that absorb them very efficiently. Experimenters used these facts to design
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This note was uploaded on 12/09/2011 for the course PHYS 344 taught by Professor Garfinkel during the Fall '08 term at Purdue University-West Lafayette.

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Lecture35 - Physics 344 Foundations of 21st Century...

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