Lect35_[Compatibility_Mode]

Lect35_[Compatibility_Mode] - Physics 344 Foundations of...

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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 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Shuo Liu Office: PHYS 283 [email protected] 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 That Shaped Physics Unit Q, Chapters 7, 10 and 11 Notices: Problem Set 11 is due next Monday before the beginning of ur last lecture session before Thanksgiving our last lecture session before Thanksgiving Midterm II at 8:00pm, Thursday, December 2 in MSEE B012
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Quantum States of an Electron in a Metal Film We chose to begin our study of quantum mechanical systems with this example because it resembles the system of a single photon in a resonant cavity that we’ve studied so carefully. Last lecture we constructed our model of an electron in an aluminum film 10 nm thick. it the interaction between the electron and the film is described by a simple 0, 0 ) 0 x x W x a < << In it the interaction between the electron and the film is described by a simple potential function () , 0 Vx xa = > here W = 4.08 eV is the work function of aluminum and = 10 nm is the where W 4.08 eV is the work function of aluminum and a 10 nm is the thickness of the film. The time-dependent Schrödinger equation governing states of the electron in the film is 2 Ψ Ψ 22 2 2 d iV x tm d x ∂Ψ = −+ Ψ = =
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In recitation yesterday we briefly considered the classical model of this system using an energy diagram of the kind you used in Physics 172. V(x) This one shows the potential energy function for the electron-film system. x E -W We consider an isolated system so its energy will be constant. The diagram also shows a horizontal line representing e energy of one possible bound state K the energy of one possible bound state of the classical electron-film system. Notice the points where E = V(x) . They are called turning points because the ystem’s energy in our approximation is the sum of the electron’s kinetic system s energy, in our approximation, is the sum of the electron s kinetic energy and the potential energy representing its interaction with the metal film. Since E = V(x) these are points where the electron’s kinetic energy is zero, i.e., where the electron comes to rest as its motion reverses. Inside the film, the kinetic energy K is positive as the electron bounces back and forth across the film. Classically, an energy E < 0 corresponds to a possible bound state of the electron-film system.
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue.

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Lect35_[Compatibility_Mode] - Physics 344 Foundations of...

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