Page 110 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch08 Elementary Physical Chemistry

Introduction to Quantum Theory 95

Schr¨odinger’s Cat.
Fig. 8.4

there is a radioactive material which emits α-particles with a half-life of
1 hour. The emitted particle triggers a contraption which releases a hammer
that shatters the glass. A half-life of an hour means that there is a 50–50
chance that an α-particle was emitted and a 50–50 chance that a particle
was not emitted. According to the Copenhagen Interpretation, the state
of the system after an hour is in a state of decay and a state of non-decay
coexisting simultaneously. Only after an observation will the combined state
collapse to either the decayed state or the non-decayed state. In the decayed
state, the cat is obviously dead and in the non-decayed state the cat is alive.
In other words, if no observation is made, the cat is simultaneously dead
and alive. “Does that make any sense?” Schr¨odinger asked.
The counter-argument was that a cat has consciousness, which acts as
an observation. The question was raised: “what if it is not a cat, what if it
is a rat, an amoeba, a bacterium?” The Schr¨odinger Cat controversy was
never resolved.
Finally, before taking up applications of Quantum Mechanics in the
next chapters, let us examine in some more detail the topics mentioned
here, namely, the de Broglie wavelength, the Uncertainty Principle, and
Probability Density.

Example 8.2. An electron moves with an energy of 10 Mev. What is the
de Broglie wavelength λ?