Page 272 - Essentials of physical chemistry

234 Essentials of Physical Chemistry

FIGURE 11.1 Erwin Rudolf Josef Alexander Schrödinger (1887–1961) was an Austrian theoretical physicist
who is famous for his wave equation treatment of quantum mechanics. He was awarded the Nobel Prize in
physics in 1933. He became a full professor at the University of Zurich in 1921 and in 1926 wrote four
extremely important papers establishing wave mechanics. He left Germany in 1933, although his parents were
Christian, and moved to various lecturing positions for several years until in 1940 he was invited to set up an
Institute for Advanced Study in Dublin. There he continued to write many papers and a small book What is Life,
with conjecture that genes are molecular, which inspired Francis Crick (of Watson and Crick) and Max
Delbruck among others to study DNA.

sophomore physics texts) and V as the conventional symbol for whatever potential energy there may
mv 2 (mv) 2 2
¼ (E tot V) ) (mv) ¼ 2m(E tot V) so
be. With that understanding, we have T ¼ ¼
2 2m
2 2
d 2px (mv) 2px 2m(E tot V) 2px
that now A sin ¼ A sin ¼ A sin or
dx 2 l h 2 l h 2 l
2
d 2m(E tot V)
c. This is where it gets interesting in that Schrödinger identified the
c ¼
dx 2 h 2
2 2
h
d
energy with a mathematical operator! Thus c ¼ (E tot V)c and further we have
2m dx 2
2 2 2 2
h
h
d d
c þ Vc ¼ E tot c and finally þ V c ¼ E tot c or H op c ¼ E tot c.
2m dx 2 2m dx 2
This has major implications in that there is a mathematical (calculus) operator H op , which
represents the total energy of a particle (in only one dimension so far) and a function c, which
incorporates the De Broglie condition and is an eigenfunction of the total energy operator. Note the
left side of the equation must be in energy units since the right side is in terms of E tot .