Chemistry Reference
In-Depth Information
1.4 PHYSICAL INTERPRETATION OF THE BASIC
PRINCIPLES
The explanation of our, so far, unusual postulates is hidden in the nature
of the experimental measurements in atomic physics. The experimentally
observed atomicity of matter (electrons and protons, carrying the ele-
mentary negative and positive charge respectively), energy (h
n
, Planck),
h, Bohr)
implies some limits in the measurements done at the microscopic level.
The direct consequence of the ineliminable interaction between the
experimental apparatus and the object of measurement at the subatomic
scale was shown by Heisenberg (1930) in his gedanken Experimente, and
is embodied in his famous uncertainty principle, which for canonically
conjugate quantities
9
can be stated in the form
l
linear momentum (h/
, De Broglie), and angular momentum (
D
x
D
p
x
h
D
E
D
t
h
ð
1
:
80
Þ
where h is the Planck constant,
D
x is the uncertainty in themeasurement of
the x-coordinate, and
D
p
x
is the uncertainty resulting in the simultaneous
measurement of the conjugate linear momentum. It can be seen that the
corresponding quantum mechanical operators do not commute:
½
x
;
p
x
¼
xp
x
p
x
x
¼
i
h
ð
1
:
81
Þ
whereas operators that are not conjugate commute; say:
½
x
;
p
y
¼
xp
y
p
y
x
¼
0
ð
1
:
82
Þ
This means that we cannot measure with the same arbitrary accuracy
two conjugated dynamical variables whose quantum mechanical
operators do not commute: the exact determination of the position
coordinate of the electron would imply the simultaneous infinite in-
accuracy in the determination of the corresponding component of the
linear momentum!
As a consequence of Heisenberg's principle, the only possible descrip-
tion of the dynamical state of a microscopic body is a probabilistic one,
and the problem is now to find the function that describes such a
probability. This was achieved by Schroedinger (1926a, 1926b, 1926c,
1926d), who assumed that particle matter (the electron) could be
9
In the sense of analytical mechanics.
