lecture_18

lecture_18 - Calculate the transmission probability T for a...

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    x V(x) 0 Calculate the transmission probability T for a particle of mass m and energy E incident from the right on the potential step shown in the figure. The energy E indicated by the dashed line is above the height V 0 of the potential step. Do this calculation by first finding the reflection probability R , then use R+T=1 to calculate the transmission probability T . V 0 E
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    7.1 Application of the Schrödinger Equation to the Hydrogen Atom 7.2 Solution of the Schrödinger Equation for Hydrogen 7.3 Quantum Numbers 7.4 Magnetic Effects on Atomic Spectra – The Normal Zeeman Effect 7.5 Intrinsic Spin 7.6 Energy Levels and Electron Probabilities CHAPTER 7 The Hydrogen Atom The Hydrogen Atom The atom of modern physics can be symbolized only through a partial differential equation in an abstract space of many dimensions. All its qualities are inferential; no material properties can be directly attributed to it. An understanding of the atomic world in that primary sensuous fashion…is impossible. - Werner Heisenberg
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    7.1: Application of the Schrödinger Equation to the Hydrogen Atom The approximation of the potential energy of the electron-proton system is electrostatic: Rewrite the three-dimensional time-independent Schrödinger Equation. For Hydrogen-like atoms (He + or Li ++ ): Replace e 2 with Ze 2 ( Z is the atomic number). Use appropriate reduced mass μ.
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    Application of the Schrödinger Equation The potential (central force) V ( r ) depends on the distance r between the proton and electron. Transform to spherical polar coordinates because of the radial symmetry. Insert the Coulomb potential into the transformed Schrödinger equation.
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    Application of the Schrödinger Equation The wave function Ψ is now a function of ( r , θ, φ ) . Equation is separable.
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This note was uploaded on 04/15/2008 for the course PHY 361 taught by Professor Alarcon during the Spring '08 term at ASU.

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lecture_18 - Calculate the transmission probability T for a...

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