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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
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.
Application of the Schrödinger Equation The wave function Ψ is now a function of ( r , θ, φ ) . Equation is separable.

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

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