# Where can a good treatment of the 'sudden' perturbation approximation be found?

Where can a good treatment of the 'sudden' perturbation approximation be found?

A lot of quantum mechanics books have very brief discussions of it but I want to see it in some detail and preferably with as many examples as possible.

Is there a book, paper, or some other place that details this approximation?

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I have a book by A.B.Migdal on qualitative methods in quantum mechanics (in Russian). Several problems can be treated by the sudden perturbation theory: radiation of suddenly accelerated charge, atom excitation in neutron-nucleus collisions, atomic transitions while beta decay of nucleus. I do not know if this book was translated. –  Vladimir Kalitvianski Aug 31 '11 at 20:59
Thanks for the suggestion. It has been translated to English and is on Amazon. Just ordered it from the library. –  BeauGeste Aug 31 '11 at 23:59
There's not much to it--- you just expand the old wavefunction in the new eigenbasis. Do you have a particular problem in mind? A traditional application is to radioactive decay. –  Ron Maimon Aug 27 '12 at 3:33
@VladimirKalitvianski: The book is translated--- I remember reading it. You should make it an answer. –  Ron Maimon Aug 27 '12 at 3:59
@RonMaimon I've asked a related question here, if you're interested. I thought this question should deserve its own answer, since only a comment was posted! –  CHM Aug 27 '12 at 5:56

Migdal's book recommended in comments is good. If you cannot find it, some Migdal's problems can be found in the standard textbook L.D. Landau and E.M. Lifshitz, Quantum mechanics, Non-relativistic theory, §41. Transitions under a perturbation acting for a finite time. There are five problems considered in the end of the section:

1. A uniform electric field is suddenly applied to a charged oscillator in the ground state. Determine the probabilities of transitions of the oscillator to excited states under the action of this perturbation.

2. The nucleus of an atom in the normal state receives an impulse which gives it a velocity $v$; the duration $\tau$ of the impulse is assumed short in comparison both with the electron periods and with $a/v$, where $a$ is the dimension of the atom. Determine the probability of excitation of the atom under the influence of such a "jolt" (A. B. Migdal 1939).

3. Determine the total probability of excitation and ionization of an atom of hydrogen which receives a sudden "jolt" (see Problem 2).

4. Determine the probability that an electron will leave the $K$-shell of an atom with large atomic number $Z$ when the nucleus undergoes $\beta$-decay. The velocity of the $\beta$-particle is assumed large in comparison with that of the $K$-electron (A. B. Migdal and E. L. Feinberg 1941).

5. Determine the probability of emergence of an electron from the $K$-shell of an atom with large $Z$ in $\alpha$-decay of the nucleus. The velocity of the $\alpha$-particle is small compared with that of the $K$-electron, but the time which it takes to leave the nucleus is small in comparison with the time of revolution of the electron (A. B. Migdal 1941, J. S. Levinger 1953).

Another application, which is very close connected to the problem 4, is the so called molecular/atomic effects in tritium beta decay. One can measure the electron neutrino mass by studying the $\beta$-electron energy spectrum in the process $\,^{3}H\to \,^{3}He^{+}+e^{-}+\bar{\nu}_{e}$ near the end-point, where the electron energy is very close to 18.6 keV.

The electron is very fast so it can hardly influence all environment around. Thus the main effect is the sudden change of the charge of nucleus. There were a lot of studies of possible molecular excitations due to such sudden perturbation. Google finds a good thesis about this subject: Natasha Doss, Calculated final state probability distributions for $T_{2}$ $\beta$-decay measurements.

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My own research led me to Bohm's Quantum Theory book, which has a chapter on the subject: