Quantum Mechanics: A Modern Development by Ballentine

In summary, Ballentine's "Quantum Mechanics: A Modern Development" is a great book that offers insights not found in other textbooks. However, it is not suitable as an introductory text and has several errors and non-standard interpretations. In particular, Ballentine's rejection of the projection postulate and use of the ensemble interpretation are questionable. Other texts, such as Landau & Lifshutz, offer a more comprehensive and accurate understanding of quantum mechanics. In summary, the conversation discusses the difference in price between two editions of the book "Quantum Mechanics: A Modern Development" and the presence of typos in different editions. The conversation also discusses the strengths and weaknesses of the book, including its coverage of lesser-known topics and its errors and

For those who have used this book


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  • #2
Can someone tell me please, what is the difference between:

- World Scientific Pub Co Inc edition (May 1998) ISBN-10: 9810227078 (Amazon price $73.00)
and
- World Scientific Pub Co Inc edition (March 1998) ISBN-10: 9810241054 (Amazon price $55.35)

and what causes such a big difference in price?

Thanks,
Zdenek
 
  • #3
This book covers a few topics I do not think are covered well, or at all, in other texts, such as state preparation. It's a great book.
 
  • #4
  • #5
Great book, that offers a few insights not found in other book. Not suitable as an introductory text.
 
  • #6
The only textbook I know which starts with the representation theory of the Galilei group (it is a book about non-relativistic QM) and considers quantisation in that context, which is the proper way to go. Very recommendable.
 
  • #7
Am I the only one who finds like a bajillion typos on every other page in this text?
 
  • #8
WannabeNewton said:
Am I the only one who finds like a bajillion typos on every other page in this text?

What printing to you have?
 
  • #9
The 1998 edition apparently.
 
  • #10
WannabeNewton said:
The 1998 edition apparently.

A particular edition of a book can have several printing runs, and typos often are corrected from one printing run to the next, without increasing the edition number or the year of publication.

For example, I have the 2006 printing of the 1998 edition of Ballentine.
 
  • #11
George Jones said:
A particular edition of a book can have several printing runs, and typos often are corrected from one printing run to the next, without increasing the edition number or the year of publication.

For example, I have the 2006 printing of the 1998 edition of Ballentine.

Awesome, thanks! I'll check out the latest printing then.
 
  • #12
I would recommend learning quantum mechanics from a textbook such as Landau & Lifshutz; Cohen-Tannoudji, Diu & LaLoë; Shankar; Sakurai & Napolitano; Weinberg; Nielsen & Chuang; Benenti, Casati & Strini; or Wiseman & Milburn; before reading Ballentine.

Ballentine makes several errors such as his discussion of the quantum Zeno effect and the outdated comments on renormalization. However, these may be incidental and minor, as even Feynman makes an elementary mistake in one appplication of Gauss's law in his justly celebrated Lectures.

What is structurally non-standard, and perhaps erroneous, is Ballentine's apparent rejection of the projection postulate mentioned in the above textbooks without replacing it with something effectively equivalent, in his discussion of filtering measurements as a means of state preparation. I do believe there are interpretations such as Bohmian mechanics, and probably many-worlds which can do without collapse or state reduction or the projection postulate (whatever one calls it). However, it is not clear to me if this is possible in Ballentine's version of the ensemble interpretation.

In particular it is unclear to me whether Ballentine's Eq 9.30 is postulated or claimed to be (partially) derived. If it is postulated, there is no problem, because it is a postulate effectively equivalent to collapse. A second mistake Ballentine seems to make is his unacknowledged use of the projection postulate in assuming that the improper mixture represented by the reduced density matrix can be treated as a proper mixture. The effective equivalence between collapse and the equivalence of proper and improper mixtures is agreed upon by Schlosshauer's 2003 review on decoherence and by Raimond and Haroche in "Exploring the Quantum".

I would also like to note that another famous book often cited for the ensemble interpretation is Peres's. There, it seems to me, instead of collapse, he postulates "blurring" of the Wigner function. I have to say I like Peres's book very much.

I do believe there is a correct presentation of the ensemble interpretation, which makes it clear that it is not at odds with the "orthodox" or "naive textbook" interpretation. This is found in Laloë's "Do we really understand quantum mechanics?" http://arxiv.org/abs/quant-ph/0209123, where it is clear that a new postulate is necessary if collapse is rejected. For those who would like to make a detailed comparison of Ballentine's and Laloë's treatments, Laloë's Eq 37 is Ballentine's Eq 9.30, if one takes into account Laloë's footnote 41.
 
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  • #13
Two more notes against the idea that collapse can be removed without replacing it with another postulate.

1) One may attempt to remove collapse by using the Stinespring theorem, which says that all completely positive operations can be thought of as unitary in a larger Hilbert space (eg. http://arxiv.org/abs/quant-ph/0512125, section 3.1.3). However, because the collapse to any particular state is random, this results in a unitary evolution that is random, in contrast to the deterministic evolution by Schroedinger's equation. So collapse cannot be removed by this method.

2) One may attempt to remove collapse by choosing to analyse all experiments so that only one measurement is made at the end (eg. http://arxiv.org/abs/0803.3237v3, footnote 15), and by giving up the principle that measurement can be used as a means of state preparation. However this causes difficulties with special relativity and the relativity of simultaneity. For example, in a Bell test a pair of measurements that is simultaneous in one reference frame will not be simultaneous in another reference frame.
 

1. What is Quantum Mechanics?

Quantum Mechanics is a fundamental theory in physics that explains the behavior of matter and energy on a microscopic scale. It describes the behavior of particles at the atomic and subatomic level, where classical mechanics fails to accurately predict their behavior.

2. Who is David Ballentine?

David Ballentine is a physicist and professor at Colorado State University. He is known for his contributions in quantum mechanics and statistical mechanics, and has authored the textbook "Quantum Mechanics: A Modern Development."

3. What makes "Quantum Mechanics: A Modern Development" different from other textbooks on the subject?

This textbook presents the concepts of quantum mechanics in a modern and intuitive way, using simple language and clear explanations. It also includes important developments in the field, such as quantum computing and quantum information theory, which are not covered in many other textbooks.

4. Is this book suitable for beginners in quantum mechanics?

While some basic knowledge of calculus and linear algebra is recommended, this textbook is designed for students with little to no background in quantum mechanics. It starts with the fundamentals and gradually builds up to more advanced topics, making it suitable for beginners.

5. What are some real-world applications of quantum mechanics?

Quantum mechanics has numerous applications in modern technology, such as in the development of transistors, lasers, and computer memory. It is also essential in fields such as chemistry, materials science, and cryptography. Additionally, research in quantum mechanics has led to the development of new technologies, such as quantum computers and quantum sensors.

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