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Introduction to Quantum Mechanics - Third Edition, by Richard Liboff

  1. Jul 20, 2003 #1

    pmb

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    "Introduction to Quantum Mechanics - Third Edition," by Richard Liboff

    Does anyone here have "Introduction to Quantum Mechanics - Third Edition," by Richard Liboff?

    I'd like some help with the way he explains Hermite functions. In the problems he says to prove a the relation

    exp(2zt - t^2) = sum(k = 0 - infinty) H_n(z)t^n/n!

    Which, of course, is done with a Taylor series expansion. It appears that Liboff wants the reader to prove this with the inormation that he gives in that section regarding H_n(z). But I don't see that its at all obvious.

    Anyone?

    Pete
     
  2. jcsd
  3. Jul 20, 2003 #2
    Liboff question

    I will look at in on Monday. I don't have the text with me now.
     
  4. Jul 20, 2003 #3

    pmb

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    Re: Liboff question

    Thank you. Much appreciated.

    Side question: Do you mind if I ask you something? Do you know the subject matter very well? I.e. have you gone through such a coursesequence or text? I'd enjoy discussing the contents of this book with someone. Are you up for it? Liboff some some weird stuff and there are errors in this verion - alot of errors I think. He also gets into some stuff which is pretty specialized especially in the problems.

    Thanks

    Pete
     
  5. Jul 20, 2003 #4
    Liboff

    Yes, I did go through parts of Liboff.

    I used it for my second quantum course and part of my atomic physics course.

    I am not an expert, I only have an undergrad., although I did do quite well in the courses. We weren't assigned many of the problems, but I wouldn't mind thinking along side you for some of them.
     
  6. Jul 20, 2003 #5

    pmb

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    Re: Liboff

    That'll be great - I'm sure that if we have the same text then one might see what the other might not be picking up on. And I hope this is the case on the Hermite polynomials

    Thanks

    Pete
     
  7. Jul 20, 2003 #6

    pmb

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    Re: Re: Liboff

    In the mean time maybe someone can help me with this -

    There is a relation which goes like this

    F(z+a) = exp[-(z+a)^2]

    Then they claim that the Taylor series expansion of this is

    F(z+a) = sum(n=0 - Inf) a^n/n! F^n(z)

    F(z+a) = sum(n=0 - Inf) a^n/n! (-1)^n H_n(z) exp(-z^2)

    Now how in the world do they get that?

    Thanks

    Pete
     
  8. Jul 20, 2003 #7

    Hurkyl

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    exp(-(z+a)^2) = exp(-z^2 - 2az - a^2)
    = exp(-z^2) exp(2z(-a) - (-a)^2)
     
  9. Jul 20, 2003 #8

    pmb

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    I'm sorry. If that was supposed to be helpful then I don't follow. What is your point?

    Pete
     
  10. Jul 20, 2003 #9

    Hurkyl

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    Then you can substitute the equation you were originally considering...

    F(z+a) = exp(-z^2) exp(2z(-a) - (-a)^2)
    = exp(-z^2) * sum(k = 0 - infinty) H_n(z) (-a)^n/n!
    = sum(n=0 - Inf) a^n/n! (-1)^n H_n(z) exp(-z^2)


    My mistake if you meant that this equation was supposed to be a hint for deriving the equation you were interested in.


    Incidentally, what is fair game to use about H_n(z)? I looked up the hermite polys on mathworld, but they essentially start with the egf you're trying to derive. Was hoping to try and help with the original question, but I don't know what you're allowed to use!
     
  11. Jul 20, 2003 #10

    pmb

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    I'm sorry but I still don't follow. My question here is how did they get this equation

    F(z+a) = sum(n=0 - Inf) a^n/n! (-1)^n H_n(z) exp(-z^2)

    from the definition of F(z+a). One can do the differention and set a a to zero etc but it doesn't tell me where the H_n(z) comes from! And that result is messy!

    Thank you

    Pete
     
  12. Jul 20, 2003 #11

    Hurkyl

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    I'm assuming

    exp(2zt - t^2) = sum(k = 0 - infinty) H_n(z)t^n/n!

    to derive the result for F(z + a)... I'm presuming that since the author has presented this formula in a problem he intends the result to be used to solve other problems, like that of F(z + a)
     
  13. Jul 30, 2003 #12

    jeff

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    Re: "Introduction to Quantum Mechanics - Third Edition," by Richard Liboff

     
  14. Jul 30, 2003 #13

    pmb

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    Re: Re: "Introduction to Quantum Mechanics - Third Edition," by Richard Liboff

    I think I see now. You're searching my posts to see where I asked a question - then you quote me thus pointing out that I don't know everything.

    never claimed I did.

    So why are you doing this jeff?

    Pmb
     
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