Physical Chemistry Third Edition

15.2 The Schrödinger Equation 657

With slit 2 closed With slit 1 closed

(a)

(b)

(c)

Detector screen which

glows where electrons

strike

Barrier with

two slits

Electron

source

Pattern of

glowing

bands

Figure 15.2 A Hypothetical Experiment with Electrons Passing through Two Slits.

(a) The Apparatus. (b) The intensity of the glow due to electrons arriving at the screen in

figure (a) with both slits open. (c) The intensity of the glow due to electrons arriving at the

screen in (a) with one slit open at a time.

15.2 The Schrödinger Equation

If electrons and other particles act like waves, they should obey a wave equation.

In 1926, Erwin Schrödinger published a series of four articles containing a wave equa-

tion for de Broglie waves, which we now call the Schrödinger equation. The first three

articles presented the time-independent version of the wave equation and applied it to

the hydrogen atom, rotation and vibration of diatomic molecules, and the effect of an

external electric field on energy levels. The time-dependent version of the equation

was reported in the fourth article.^4

Erwin Schrödinger, 1887–1961, was an
Austrian physicist who shared the 1933
Nobel Prize in physics with P. A. M.
Dirac, who pioneered the development
of relativistic quantum mechanics.

(^4) The time-independent equations were presented inAnn. Physik, 79 , 361 (1926), 79 , 489 (1926), and
80 , 437 (1926), and the time-dependent equation was presented inAnn. Physik, 81 , 109 (1926).