retical explanation of this behavior it was necessary to assume
that the energy of a mechanical system cannot assume any
sort of value, but only certain discrete values whose mathe-
matical expressions were always dependent upon Planck's
constant h.
Moreover, this conception was essential for the
theory of the atom (Bohr's theory).
For the transitions of
these states into one another,--with or without emission or
absorption of radiation,--no causal laws could be given, but
only statistical ones; and, a similar conclusion holds for the
radioactive decomposition of atoms, which decomposition was
carefully investigated about the same time.
For more than
two decades physicists tried vainly to find a uniform inter-
pretation of this " quantum character " of systems and
phenomena.
Such an attempt was successful about ten years
ago, through the agency of two entirely different theoretical
methods of attack.
We owe one of these to Heisenberg and
Dirac, and the other to de Broglie and Schr6dinger.
The
mathematical equivalence of the two methods was soon recog-
nized by Schr6dinger.
I shall try here to sketch the line of
thought of de Broglie and Schr6dinger, which lies closer to the
physicist's method of thinking, and shall accompany the
description with certain general considerations.
The question is first: How can one assign a discrete suc-
cession of energy value H, to a system specified in the sense
of classical mechanics (the energy function is a given function
of the co6rdinates q~ and the corresponding momenta p,)?
Planck's constant h relates the frequency
H,/h
to the energy
values H,.
It is therefore sufficient to give to the system a
succession of discrete
frequency
values.
This reminds us of
the fact that in acoustics, a series of discrete frequency values
is co6rdinated to a linear partial differential equation (if

March, I936.]
PHYSICS AND REALITY.
373
boundary values are given) namely the sinusoidal periodic
solutions.
In corresponding manner, Schr6dinger set himself
the task of co6rdinating a partial differential equation for a
scalar function ~b to the given energy function
~(qr, Pr),
where
the q~ and the time t are independent variables.
In this he
succeeded (for a complex function $) in such a manner that
the theoretical values of the energy
Ho,
as required by the
statistical theory, actually resulted in a satisfactory manner
from the periodic solution of the equation.
To be sure, it did not happen to be possible to associate a
definite movement, in the sense of mechanics of material
points, with a definite solution ¢(qr, t) of the Schr6dinger
equation.
This means that the ~ function does not deter-
mine, at any rate
exactly,
the story of the qr as functions of the
time t.
According to Born, however, an interpretation of the
physical meaning of the ~ functions was shown to be possible
in the following manner: Sf (the square of the absolute value
of the complex function ~) is the probability density at the
point under consideration in the configuration-space of the
qr, at the time t.
It is therefore possible to characterize the

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