Physical Chemistry , 1st ed.

where the potential energy is high, even if the potential energy is greater than

the total energy of the particle. Furthermore, the mathematical form of this

wavefunction guarantees that it will not equal zero for any finite value ofx.

This means that there is a nonzero probability that a particle with this wave-

function will exist at the other side of the box, even though the total energy of

the particle is less than the potential barrier. This is illustrated qualitatively in

Figure 10.9. Classically, if the barrier were higher than the total energy, the par-

ticle couldn’t exist on the other side of the barrier. Quantum mechanically, it

can. This is called tunneling.

Tunneling is a simple yet profound prediction of quantum mechanics. After

these conclusions were announced, in 1928 Russian scientist George Gamow

used tunneling as an explanation of alpha decay in radioactive nuclei. There

had been speculation about exactly how the alpha particle (a helium nucleus)

could escape the huge potential energy barrier of the other nuclear particles.

More recently, we have seen the development of the scanning tunneling mi-

croscope (STM). This simple device, illustrated in Figure 10.10, uses tunneling

298 CHAPTER 10 Introduction to Quantum Mechanics

x  0 x  a

x-axis

V  K () V  

  0



V  0 V  0

Energy

Figure 10.9 Due to the noninfinite height and
depth of the potential energy barrier, the wave-
function has a nonzero probability of existing on
the other side of the barrier. Alpha particle decay
and small gaps between two surfaces are two sys-
tems where tunneling occurs.

Data processing

and display

Control voltages for piezotube

Distance control

and scanning unit

Tunneling

current

amplifier

Piezoelectric tube

with electrodes

Tunneling

voltage

Tip

Sample

Figure 10.10 A commercial scanning tunnel-
ing microscope (STM). Invented in the early 1980s,
STMs take advantage of a quantum-mechanical
phenomenon.