Classical versus quantum mechanics

Quantum mechanics is the branch of physics that describes the behaviour of very small particles such as electrons, atoms and photons, using wave functions and probabilities instead of exact paths.

Importance of quantum mechanics

Classical mechanics works for large objects but fails at atomic scale. It could not explain:

• black-body radiation, the photoelectric effect and the Compton effect;
• the stability of atoms and their sharp spectral lines;
• the specific heat and electrical conductivity of metals.

Quantum mechanics explains all of these. For electrical engineering materials it is essential because it explains:

• energy bands and why some solids are conductors, others semiconductors or insulators;
• effective mass, holes and carrier concentration in semiconductors;
• tunneling, used in tunnel diodes, flash memory and the STM;
• the operation of lasers, LEDs, solar cells, transistors and superconductors.

Classical versus quantum mechanics

Examples

• Ball in a box vs electron in a well: a ball in a box can have any speed, even zero. An electron in a 0.1 nm well can only have $E_n = n^2(37.7\text{ eV})$ and can never be at rest.
• Barrier: a car that cannot climb a hill never appears on the other side, but an electron with 7 eV can pass through a 10 eV, 3 nm oxide layer between copper wires with a small probability.
• Wavelength: a 50 g golf ball at 20 m/s has $\lambda = 6.6\times10^{-34}$ m, far too small to observe, so classical mechanics is enough; an electron accelerated through 100 V has $\lambda = 0.123$ nm, comparable to atomic spacing, so its wave nature (electron diffraction) is clearly seen.

Classical mechanics is a limiting case of quantum mechanics for large masses and large quantum numbers (correspondence principle).