Transcription of Chapter 9 Angular Momentum Quantum Mechanical …
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Chapter 9 Angular Momentum Quantum Mechanical …
Chapter 9 Angular MomentumQuantum Mechanical Angular Momentum OperatorsClassical Angular Momentum is a vector quantity denoted~L=~rX~p. A common mnemonicto calculate the components is~L= ^i^j^kxyzpxpypz = ypz zpy ^i+ zpx xpz ^j+ xpy ypx ^j=Lx^i+Ly^j+Lz^j:Let's focus on one component of Angular Momentum , sayLx=ypz the rightside of the equation are two components of position and two components of linear mechanically, all four quantities are operators. Since the product of two operators is anoperator, and the di erence of operators is another operator, we expect the components of angularmomentum to be operators.
= i„hL z: The other two relations, £ L y; L z ⁄ = i„h L x and £ L z; L x ⁄ = i„h L y can be calculated using similar procedures. A Representation of Angular Momentum Operators We would like to have matrix operators for the angular momentum operators L x; L y, and L z. In the form L x; L y, and L z, these are abstract operators in an ...
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