Electronic Properties of Materials/Quantum Mechanics for Engineers/Quantum Mechanics Overview

This is the first chapter of the first section of the textbook Electronic Properties of Materials.

Quantum Mechanics Overview

The origins of quantum mechanics came about in the quantum revolution from 1890 to 1930. During this time several new discoveries facilitated this transition.

1. Light has particle nature in addition to wave nature.
2. Light (photons) and matter are found to interact and develop theory of atomic structure.
3. Matter has wave nature in addition to particle nature.

These discoveries led to the birth of modern quantum mechanics.

Light Has A Particle Nature

As early as 1877, Boltzmann proposed that energy was not continuous, but rather discretized. In 1905, Raleigh-Jean applied this to black bodies, a perfect radiator where radiation is emitted form vibrating atoms that act as little dipoles to create the Raleigh-Jean Theory. This theory takes ${\textstyle \langle E\rangle }$ as the expectation value of the energy giving:

$$\langle E\rangle ={\int _{0}^{\infty }Ee^{-\beta E}\operatorname {d} \!E \over \int _{0}^{\infty }e^{-\beta E}\operatorname {d} \!E}$$

This distribution is energy times the distribution over the partition function which produces $kT$. While this generally follows experimental results at large wavelengths, at shorter wavelengths the prediction diverges from experimental results.

In 1901, Plank also took the existing theory and modified it to replace continuous energy with discrete energies giving:

$$E=\eta h\nu =\eta h{c \over \lambda }$$

This 'fix' for the UV catastrophe was completed by incorporating Wein's Law (1893).

Discrete Energies

When we think about energies they may look continuous but they are actually discretized. Furthermore, in 1905 Einstein said that not only is energy quantized, but so is electromagnets. in 1887, Hertz showed through his photoelectric effect experiment