Introduction to Quantum Mechanics - Third Edition, by Richard Liboff

In summary, the conversation is about the textbook "Introduction to Quantum Mechanics - Third Edition" by Richard Liboff. The original poster is seeking help with understanding Hermite functions and a relation involving them. Others in the conversation offer to help, with one person mentioning they have gone through parts of the textbook. The conversation then shifts to discussing a specific equation and how to derive it, with the original poster expressing confusion about where the Hermite polynomials come into play. The conversation ends with a comment about someone searching the original poster's previous posts.
  • #1
pmb
"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
 
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  • #2
Liboff question

I will look at in on Monday. I don't have the text with me now.
 
  • #3


Originally posted by sdeliver645
I will look at in on Monday. I don't have the text with me now.

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 - a lot of errors I think. He also gets into some stuff which is pretty specialized especially in the problems.

Thanks

Pete
 
  • #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.
 
  • #5


Originally posted by sdeliver645
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.

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
 
  • #6


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
 
  • #7
exp(-(z+a)^2) = exp(-z^2 - 2az - a^2)
= exp(-z^2) exp(2z(-a) - (-a)^2)
 
  • #8
Originally posted by Hurkyl
exp(-(z+a)^2) = exp(-z^2 - 2az - a^2)
= exp(-z^2) exp(2z(-a) - (-a)^2)

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

Pete
 
  • #9
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!
 
  • #10
Originally posted by Hurkyl
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!


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
 
  • #11
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)
 
  • #12


Originally posted by pmb
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.
 
  • #13


Originally posted by jeff

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
 

1. What is quantum mechanics?

Quantum mechanics is a branch of physics that studies the behavior and interactions of subatomic particles, such as electrons and photons. It is used to describe the fundamental laws and principles that govern the behavior of matter and energy at a microscopic level.

2. Who is Richard Liboff?

Richard Liboff is a physicist and professor emeritus at Cornell University. He is known for his contributions to the field of condensed matter physics and has authored several textbooks, including "Introduction to Quantum Mechanics - Third Edition."

3. What topics are covered in "Introduction to Quantum Mechanics - Third Edition"?

This textbook covers topics such as the mathematical foundations of quantum mechanics, quantum dynamics, angular momentum, perturbation theory, and the quantum theory of radiation. It also includes chapters on the application of quantum mechanics to atomic, molecular, and solid state systems.

4. Is "Introduction to Quantum Mechanics - Third Edition" suitable for beginners?

While some prior knowledge of physics and mathematics is recommended, "Introduction to Quantum Mechanics - Third Edition" is designed to be accessible to students with no previous background in quantum mechanics. It provides a thorough introduction to the subject and includes many examples and exercises to aid in understanding.

5. What makes the third edition of "Introduction to Quantum Mechanics" different from previous editions?

The third edition of "Introduction to Quantum Mechanics" includes updated content to reflect advancements in the field, as well as additional examples and exercises. It also features new sections on topics such as quantum computing and quantum information theory.

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