Manfra20-2011

Manfra20-2011 - CHAPTER 7 The Hydrogen Atom 7.1 Application...

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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 Zeeman Effect 7.5 Intrinsic Spin 7.6 Energy Levels and Electron Probabilities CHAPTER 7 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 Werner Heisenberg (1901-1976)
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The wave function must be a function of all three spatial coordinates. Now consider momentum as an operator acting on the wave function in three dimensions: 6.5: Three-Dimensional Infinite-Potential Well So the three-dimensional Schrödinger wave equation is
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The 3D infinite potential well 2 2 2 2 2 2 2 2 2 y x z x y z n n n E m L L L π = + + h It’s easy to show that: ( 29 2 2 2 2 2 2 2 x y z E n n n mL = + + h When the box is a cube: ( , , ) sin( ) sin( ) sin( ) x y z x y z A k x k y k z ψ = / x x x k n L = where: / y y y k n L = / z z z k n L = and:
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This note was uploaded on 04/23/2011 for the course PHYS 342 taught by Professor Staff during the Spring '08 term at Purdue.

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Manfra20-2011 - CHAPTER 7 The Hydrogen Atom 7.1 Application...

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