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1.3.4 Functions of Operators
In the previous sections I have discussed linear operators and special
subclasses of these operators such as Hermitean and unitary operators.
When we write down the Hamilton operator of a quantum mechanical
system we will often encounter functions of operators, such as the onedimensional potential V (ˆx) in which a particle is moving. Therefore it
is important to know the definition and some properties of functions of
operators. There are two ways of defining functions on an operator, one
works particularly well for operators with a complete set of eigenvectors
(Definition 26), while the other one works bests for functions that can
be expanded into power series (Definition 27).
1.3.4 Functions of Operators
In the previous sections I have discussed linear operators and special
subclasses of these operators such as Hermitean and unitary operators.
When we write down the Hamilton operator of a quantum mechanical
system we will often encounter functions of operators, such as the onedimensional potential V (ˆx) in which a particle is moving. Therefore it
is important to know the definition and some properties of functions of
operators. There are two ways of defining functions on an operator, one
works particularly well for operators with a complete set of eigenvectors
(Definition 26), while the other one works bests for functions that can
be expanded into power series (Definition 27).
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