FUNDAMENTAL IDEA OF WAVE MECHANICS 309 low, it is very difficult, without further going into details, to convey a proper conception of the success or failure of these classical-mechanical im- ages of the atom On the one hand, Hamiltons principle in particular proved to be the most faithful and reliable guide, which was simply indispensable on the other hand one had to suffer, to do justice to the facts, the rough interference of entirely new incomprehensible postulates, of the so-called quantum conditions and quantum postulates Strident disharmony in the symphony of classical mechanics- yet strangely familiar -played as it were on the same instrument. In mathematical terms we can formulate this as fol- lows: whereas the Hamilton principle merely postulates that a given integral must be a minimum, without the numerical value of the minimum being established by this postulate, it is now demanded that the numerical value of the minimum should be restricted to integral multiples of a universal natu- ral constant, Planck's quantum of action. This incidentally. The situation was fairly desperate. Had the old mechanics failed completely, it would not have been so bad. The way would then have been free to the development of a new system ofmechanics. As it was, one was faced with the difficult task of saving the soul of the old system, whose inspiration clearly held sway in this microcosm, while at the same time flattering it as it were into accepting th quantum conditions not as gross interference but as issuing from its own innermost essence The way out lay just in the possibility, already indicated above, of attrib uting to the Hamilton principle, also, the operation of a wave mechanism on which the point-mechanical processes are essentially based, just as one had long become accustomed to doing in the case of phenomena relating to light and of the Fermat principle which governs them. Admittedly, the in- dividual path of a mass point loses its proper physical significance and be comes as fictitious as the individual isolated ray of light. The essence of the theory, the minimum principle, however, remains not only intact, but reveals its true and simple meaning only under the wave-like aspect, as already ex- plained. Strictly speaking, the new theory is in fact not new, it is a completely organic development, one might almost be tempted to say a more elaborate exposition, of the old theory How was it then that this new more "elaborate"exposition led to notably different results; what enabled it, when applied to the atom, to obviate diffi- culties which the old theory could not solve? What enabled it to render gross interference acceptable or even to make it its own? Again, these matters can best be illustrated by analogy with optics. QuiteFUNDAMENTAL IDEA OF WAVE MECHANIC S 309 Now, it is very difficult, without further going into details, to convey a proper conception of the success or failure of these classical-mechanical im￾ages of the atom. On the one hand, Hamilton’s principle in particular proved to be the most faithful and reliable guide, which was simply indispensable; on the other hand one had to suffer, to do justice to the facts, the rough interference of entirely new incomprehensible postulates, of the so-called quantum conditions and quantum postulates. Strident disharmony in the symphony of classical mechanics - yet strangely familiar - played as it were on the same instrument. In mathematical terms we can formulate this as fol￾lows: whereas the Hamilton principle merely postulates that a given integral must be a minimum, without the numerical value of the minimum being established by this postulate, it is now demanded that the numerical value of the minimum should be restricted to integral multiples of a universal natu￾ral constant, Planck’s quantum of action. This incidentally. The situation was fairly desperate. Had the old mechanics failed completely, it would not have been so bad. The way would then have been free to the development of a new system ofmechanics. As it was, one was faced with the difficult task of saving the soul of the old system, whose inspiration clearly held sway in this microcosm, while at the same time flattering it as it were into accepting the quantum conditions not as gross interference but as issuing from its own innermost essence. The way out lay just in the possibility, already indicated above, of attrib￾uting to the Hamilton principle, also, the operation of a wave mechanism on which the point-mechanical processes are essentially based, just as one had long become accustomed to doing in the case of phenomena relating to light and of the Fermat principle which governs them. Admittedly, the in￾dividual path of a mass point loses its proper physical significance and be￾comes as fictitious as the individual isolated ray of light. The essence of the theory, the minimum principle, however, remains not only intact, but reveals its true and simple meaning only under the wave-like aspect, as already ex￾plained. Strictly speaking, the new theory is in fact not new, it is a completely organic development, one might almost be tempted to say a more elaborate exposition, of the old theory. How was it then that this new more "elaborate" exposition led to notably different results; what enabled it, when applied to the atom, to obviate diffi￾culties which the old theory could not solve? What enabled it to render gross interference acceptable or even to make it its own? Again, these matters can best be illustrated by analogy with optics. Quite