Quantum Mechanics: A Modern Development by Ballentine

[micromass]

• Author: Leslie Ballentine
• Title: Quantum Mechanics: A Modern Development
• Amazon Link: https://www.amazon.com/dp/9810227078/?tag=pfamazon01-20

 

[Frimus]

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

 

[Jorriss]

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.

 

[Frimus]

I have resolved the mystery. ISBN-10: 9810227078 edition is a hardcover. Amazon erroneously lists it as a paperback.
see: Quantum Mechanics A Modern Development

 

[xepma]

Great book, that offers a few insights not found in other book. Not suitable as an introductory text.

 

[DrDu]

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.

 

[WannabeNewton]

Am I the only one who finds like a bajillion typos on every other page in this text?

 

[Daverz]

Am I the only one who finds like a bajillion typos on every other page in this text?

What printing to you have?

 

[WannabeNewton]

The 1998 edition apparently.

 

[George Jones]

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.

 

[WannabeNewton]

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.

 

[atyy]

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.

 

[atyy]

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.