I von Neumann Measurement Scheme

[Kyuubi]

Greetings,
I would like to ask something about the von Neumann measurement scheme in the context of Time~symmetric QM and weak measurements in the popular Aharonov, Bergmann, and Lebowitz (1955, ABL) paper and the Aharonov, Albert, and Vaidman (1988, AAV) paper.

Particularly in the latter paper, they say "In quantum theory, the result of a measurement of a variable $A$ which has discrete eigenvalues $a_i$ must necessarily be one of those values. The Hamiltonian of the standard measurement procedure is

$H = -g(t)qA,$

where $g(t)$ is a normalized function with a compact support near the time of measurement, and $q$ is a canonical variable of the measuring device with a conjugate momentum $\pi$".

For this, they reference von Neumann's Mathematical Foundations of Quantum Mechanics and say that "The Hamiltonian [above] is the effective Hamiltonian of a Stern-Gerlach measuring device..."

My problem is that all citations of von Neumann's book just site the book without the chapter. I am unable to find relevant discussion to learn about how this Hamiltonian is brought about. Would anyone kindly share resources for learning about this or even assist in finding the relevant part in von Neumann's book?

 

[Demystifier]

The relevant part of the von Neumann's book is Chapter VI "The Measuring Process". But this is not the best way to learn it, it is explained much better in many later books and papers. One good example is https://arxiv.org/abs/1406.5535 Sec. 6.1.

 

[Kyuubi]

I thank you profusely.