
56 Nanosensors: Physical, Chemical, and Biological
Equations 1.12 and 1.13 show that the phase of the electron wave function
undergoes uniform variation in the metals. The wavelength is λ = 2π/k.
Higher-energy electrons have a larger frequency and smaller wavelength.
When a high-energy electron wave stumbles upon the boundary of the
metal, it “leaks out” a very small amount. The “intensity” of the electron
wave declines as a function of distance from the boundary. Mathematically
speaking, the argument of the exponential function becomes real and the
electron wave function decays. (For imaginary arguments, the wave func-
tion will have o