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## Über dieses Buch

This work was first published in 1947 in German under the title "Re­ chenmethoden der Quantentheorie". It was meant to serve a double purpose: to help both, the student when first confronted with quantum mechanics and the experimental scientist, who has never before used it as a tool, to learn how to apply the general theory to practical problems of atomic physics. Since that early date, many excellent books have been written introducing into the general framework of the theory and thus indispensable to a deeper understanding. It seems, however, that the more practical side has been somewhat neglected, except, of course, for the flood of special monographs going into broad detail on rather restricted topics. In other words, an all-round introduction to the practical use of quantum mechanics seems, so far, not to exist and may still be helpful. It was in the hope of filling this gap that the author has fallen in with the publishers' wish to bring the earlier German editions up to date and to make the work more useful to the worldwide community of science students and scientists by writing the new edition in English. From the beginning there could be no doubt that the work had to be much enlarged. New approximation methods and other developments, especially in the field of scattering, had to be added. It seemed necessary to include relativistic quantum mechanics and to offer, at least, a glimpse of radiation theory as an example of wave field quantization.

## Inhaltsverzeichnis

### I. General Concepts

Abstract
If the normalization relation
$$\int {{d^3}} x\psi * \psi = 1$$
(1.1)
is interpreted in the sense of probability theory, so that $${d^3}x\psi * \psi$$ is the probability of finding the particle under consideration in the volume element d3x, then there must be a conservation law. This is to be derived. How may it be interpreted classically?
Siegfried Flügge

### II. One-Body Problems without Spin

Abstract
One-dimensional problems, though in a sense oversimplifications, may be used with advantage in order to understand the essential features of quantum mechanics. They may be derived from the three-dimensional wave equation,
$$- {\mkern 1mu} \frac{{{\hbar ^2}}}{{2m}}{\nabla ^2}\psi = + V(x,t)\psi - \frac{\hbar }{i}\frac{{\partial \psi }}{{\partial t}},$$
(A.1)
if the potential depends upon only one rectangular coordinate x, by factorization:
$$\psi = {e^{i({k_2}y + {k_3}z)}}{\mkern 1mu} \varphi (x,t).$$
(A.2)
Siegfried Flügge

### III. Particles with Spin

Abstract
A particle of spin 1/2 has three basic properties:
1.
It bears an intrinsic vector property that does not depend upon space coordinates.

2.
This vector is an angular momentum (= spin) to be added to the orbital momentum of the particle.

3.
If one of the components of the spin is measured, the result can be only one of its two eigenvalues, +1/2ħ or −1/2ħ.

Siegfried Flügge

### IV. IV. Many-Body Problems

Abstract
Two particlcs arc fixed on a circle with a mutual repulsion given by
$$V({\varphi _1},{\varphi _2})\, = \,{V_0}\,\cos ({\varphi _1}, - {\varphi _2})$$
(148.1)
to simulate e.g. the Coulomb repulsion between the two helium electrons in the ground state. The conservation of angular momentum shall be derived, and the relative motion of the particles discussed.
Siegfried Flügge

### V. V. Non-Stationary Problems

Abstract
Given an atomic system with only two stationary states ∣1〉 and ∣2〉 and energies ħω1 <ħω2. At the time t = 0, the system being in its ground state, a perturbation W not depending upon time is switched on. The probability shall be calculated of finding the system in either state at the time t.
Siegfried Flügge

### VI. The Relativistic Dirac Equation

Abstract
Remark. In this chapter we use the fourth coordinate x4=ict and Euclidian metric. Greek subscripts (e.g. x μ ) run overμ =1,2,3,4, Latin subscripts (xk) over k = 1,2,3, only.
Siegfried Flügge