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I Exponential operators

  1. Apr 28, 2016 #1

    dyn

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    If I rearrange an equation invoving exponentials of operators and I take ex to the opposite side of the equation it becomes e-x. What happens if I try to take eA to the opposite side ? I know a exponential of operators can be expanded as a Taylor series which involves products of matrices but can this be inverted ?
     
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  3. Apr 28, 2016 #2

    micromass

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    Yes, ##(e^{A})^{-1} = e^{-A}##
     
  4. Apr 28, 2016 #3

    dyn

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    Thanks. Are there any conditions for that to apply ? To invert an ordinary matrix requires a non-zero determinant. Are there any conditions on the operator/matrix in the exponential ? Also when taking the exponential over to the other side of the equation I presume order matters in case any operators do not commute ?
     
  5. Apr 28, 2016 #4

    micromass

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    No. As long as ##e^A## exists (which it always does if ##A## is a bounded operator), then the above applies.

    Yes.
     
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