SCHRODINGER AND HEISENBERG HOW TO

The special system of algebraic equations, which, a special case, connects the matrices of the position and impulse co-ordinates with the matrix of the Hamilton function, and which the authors call 'equations of motion'', will be completely solved by assigning the auxiliary rГґle to a definite The provisional indefiniteness of the relation lies in the fact that we can assign the auxiliary rГґle to anДЄfter matrices are thus constructed in a very general way, so as to satisfy the general rules, I will show the following in S 4. (In other words: the particular Hamilton function does not enter into the connecting law.) However, the relation is still indefinite of an arbitrary complete orthogonal system of functions having for domain entire configuration space (N.B.-not 'pq-space'', but ' q-space''). System considered, but is the same for all mechanical systems. This relation of matrices to functions is general it takes no account of the special mechanical

SCHRODINGER AND HEISENBERG HOW TO

I will first show (S S 2 and 3) how to each function of the position- and momentum-co-ordinates there may be related a matrix in such a manner, that these matrices, in every case, satisfy the formal calculating rules of Born and Heisenberg (among which I also reckon the so-called 'quantum condition'' or 'interchange rule'' see below). (The relation is this: to one position-, one momentum-co-ordinate, or to one function of these corresponds Heisenberg's theory connects the solution of a problem in quantum mechanics with the solution of a system of an infinite number of algebraic equations, in which the unknowns-infinite matrices-are allied to the classical position- and momentum-co-ordinates of the mechanical system, and functions of these, and obey peculiar calculating rules. From the formal mathematical standpoint, one might well speak of the identity of the two theories. In what follows the very intimate inner connection between Heisenberg's quantum mechanics and my wave mechanics will be disclosed. This principle and this differential equation replace the equations of motion and the quantum conditions of the older 'classical quantum theory''. In place of a process described in terms of a finite number of dependent variables occurring in a finite number of total differential equations, we have a continuous field-like process in configuration space, which is governed by a single partialДifferential equation, derived from a principle of action. On the other hand, wave mechanics shows just the reverse tendency it is a step from classical point-mechanics towards a continuum-theory. The authors themselves describe the theory as a 'true theory of a discontinuum''. In Heisenberg's work the classical continuous variables are replaced by systems of discrete numerical quantities (matrices), which depend on a pair of integral indices, and are defined by algebraicД®quations. Above all, however, the departure from classical mechanics in the two theories seems to occur in diametrically opposed directions. That is really very remarkable, because starting-points, presentations, methods, and in fact the whole mathematical apparatus, seem fundamentally different. I refer, in particular, to the peculiar 'half-integralness'' which arises in connection with the oscillatorДЄnd the rotator. SchrГ¶dinger (1984c) 98.Д¬onsidering the extraordinary differences between the starting-points and the concepts of Heisenberg's quantum mechanics and of the theory which has been designated 'undulatory'' or 'physical'' mechanics, and has lately been described here, it is very strange that these two new theories agree with one another with regard to the known facts, where they differ from the old quantum theory.

Gesammelte Abhandlungen / Collected Works, E. SchrГ¶dinger, Glazgow (1928) 45.ДЄbhandlungen zur Wellenmechanik, E.

(translation into English) Collected Papers on Wave Mechanics by E. Гњber das VerhГ¤ltnis der Heisenberg Born Jordanischen Quantenmechanik zu der meinen / On the Relation Between the Quantum Mechanics of Heisenberg, Born, and Jordan, and that of SchrГ¶dingerДЄnnalen der Physik. Dirac 'for the discovery of new productive forms of atomic theory'' About Contents Introduction Synopsis Search Subject Index Summaries Texts Our basis ketsДЄre time-independent but quantum states are built from them with time-dependent coeп¬ѓcients: The Schr Г¶ dinger picture is the one we are used to. To d n ( t ) = e i E n ( 0 ) t в€• в„Џ c n ( t )), weДid something which has a rather fancy name: we switched to the interaction picture. When at the start we, for convenience, absorbed the time dependence due to

Schrodinger and heisenberg