Quantum Mechanics
Quantum mechanics is a description of the behavior of matter and energy on a small scale--a scale small enough that the discrete or discontinuous nature of all matter and radiation becomes noticeable.
The difference between classical mechanics and quantum mechanics is analogous to the difference between a ramp and a staircase. The ramp (classical theory) is continuous and an object may assume any position on it. If the height of the object represents its energy, it may have any value. In moving up or down the ramp (gain or loss of energy), the object passes through all intermediate energy states in a continuous increase or decrease. An object placed on a staircase (quantum theory) can occupy only particular, discrete positions. Each step represents a quantum of energy. According to quantum theory, the object can increase or decrease its energy level only by absorbing or emitting exactly enough energy to permit it to exist at another allowed energy level. In making a "quantum jump" the object simply does not exist between allowed levels.
If the steps are sufficiently small, the description of the staircase is virtually the same as the description of the ramp. In reality, the individual quanta are extremely minute, so that for macroscopic phenomena the discontinuous nature is not noticeable. The energy E in a single quantum of radiation of frequency nu is given by E = h (nu), where h is Planck's constant. Classical physics assumed h = 0; in quantum physics it has the very small but nonzero value of approximately 6.62 X (10 to the power of -34) joule-seconds.
Development of Quantum Mechanics
Before the 20th century it was thought that matter and radiation could be described in a continuous fashion--that an object could be of any size and could absorb or emit radiation of any energy. By the beginning of the 20th century, much evidence showing the discrete nature of phenomena, especially those involving atomic structure and spectra, was available. This evidence provided the impetus for the development of quantum mechanics. The new quantum mechanics was able to explain a multitude of physical phenomena that classical physics could not and so became quite rapidly accepted. Quantum mechanics, however, requires quite a different set of assumptions than does the continuum classical mechanics, even though the quantum description always agrees with the classical description for systems that are large enough. For extremely large systems and for those traveling near the speed of light, the classical mechanics is also inadequate, and the theory of relativity, proposed by Albert Einstein in 1905, is needed. Quantum mechanics and the theory of relativity together utterly upset the foundations of the classical physics. The new theories have posed philosophical problems, many of which continue to be investigated.