Lect25_AngMom1 - Lecture 25 Introduction to the Quantum...

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Lecture 25: Introduction to the Quantum Theory of Angular Momentum Phy851 Fall 2009
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Goals 1. Understand how to use different coordinate systems in QM (cartesian, spherical,…) 2. Derive the quantum mechanical properties of Angular Momentum Use an algebraic approach similar to what we did for the Harmonic Oscillator 3. Use the resulting theory to treat spherically symmetric problems in three dimensions Calculating the Hydrogen atom energy levels will be our target goal
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Motion In 3Dimensions For a particle moving in three dimensions, there is a distinct quantum state for every point in space. Thus each position state is now labeled by a vector Vector operators are really three operators Coordinate system not unique: For example, we could use spherical coordinates R X v r x r z y x e Z e Y e X R r r r r + + = Z Y X , , Scalar Operators Ordinary Vectors z y x e e e r r r , , ) , ( Φ Θ = r e R R r r Φ Θ , , R Scalar Operators z y x r e e e e r r r r Θ + Φ Θ + Φ Θ = Φ Θ cos sin sin cos sin ) , (
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