Exponential operators

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  • #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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  • #2
micromass
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Yes, ##(e^{A})^{-1} = e^{-A}##
 
  • #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 ?
 
  • #4
micromass
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Thanks. Are there any conditions for that to apply ?

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

Also when taking the exponential over to the other side of the equation I presume order matters in case any operators do not commute ?

Yes.
 

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