1. Reading: Chapter 1 in Shankar
PHY 712 Quantum Mechanics
12-12:50 PM MWF Olin 103
Plan for Lecture 2:
Reading: Chapter 1 in Shankar
Properties of finite-dimensional linear vector spaces
Eigenvalue properties of special operators
Singular value decomposition
Evaluation of operators and functions of operators
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PHY 741 Fall Lecture 2

2. Schedule additional office hours by
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PHY 741 Fall Lecture 2

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5. The notion of linear vector spaces is very useful for describing quantum mechanics. First consider a finite (n) dimensional vector space expressed in terms of an orthonormal basis.
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PHY 741 Fall Lecture 2

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7. Example:
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PHY 741 Fall Lecture 2

8. Special case of “commuting” Hermitian operators
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PHY 741 Fall Lecture 2

9. Special case of “commuting” Hermitian operators -- continued
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PHY 741 Fall Lecture 2

10. Special case of “commuting” Hermitian operators -- example
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PHY 741 Fall Lecture 2

11. Digression – singular value decomposition
Some useful properties of matrices
12/02/2016
PHY 711 Fall Lecture 37

12. Singular value decomposition
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PHY 711 Fall Lecture 37

13. Singular value decomposition -- continued
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PHY 711 Fall Lecture 37

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PHY 711 Fall Lecture 37

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16. Example: = =
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PHY 711 Fall Lecture 37

17. Note that SVD can be applied to rectangular matricesUT
12/02/2016
PHY 711 Fall Lecture 37

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19. Functions of Operators
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PHY 741 Fall Lecture 2

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21. Functions of multiple operators
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PHY 741 Fall Lecture 2