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Obtaining a more accurate calculator?

  1. Jun 18, 2012 #1
    I'm trying to calculate relativistic photon energy shifts, and I have to use [tex]e^{\frac{x}{c^{2}}}[/tex]
    However,since I'm dealing with the speed of light, the exponent becomes extremely small and my TI-84 gives me a nonsensical value.

    Could anyone recommend a more accurate calculator?
     
    Last edited: Jun 18, 2012
  2. jcsd
  3. Jun 18, 2012 #2

    haruspex

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    If [tex]\frac{x}{c^{2}}[/tex] is that small, how inaccurate would it be to approximate the answer as [tex]1+\frac{x}{c^{2}}[/tex]?
     
  4. Jun 18, 2012 #3
    so you think i should use maclaurin's expansion?
     
  5. Jun 18, 2012 #4
    Yes, just cut the first two terms. By the Lagrange form of the remainder, we obtain that an upper bound for the error can be given by [itex]\displaystyle \frac{x^{k+1}}{(k+1)!c^{2k+2}}[/itex] in a Taylor polynomial of degree k. Taking k as two (the above case), we obtain that an upper bound of the error is [itex]\displaystyle \frac{x^3}{6c^6}[/itex], which, as long as [itex]x\leq c[/itex], is accurate to at least 5 decimal places.
     
  6. Jun 18, 2012 #5

    haruspex

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    That would be taking the first 3 terms, no? Sure, that should be fine, but the first two terms might be enough. How big is x/c2, and how accurate do you need the answer to be?
     
  7. Jun 18, 2012 #6
  8. Jun 18, 2012 #7
    my answer would be in the range of 10^-11 eV.
     
  9. Jun 18, 2012 #8
  10. Oct 29, 2012 #9

    haruspex

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    x/c2 has units? Doesn't seem right. What exactly does x represent?
     
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