(c) Dr Paul Kinsler. [Acknowledgements & Feedback]

This is part of an information maze -- see the index-file for the full picture.

Quantum Confinement

Anything described by quantum-mechanics has some wave -like properties, as described by its wave-function. Trapping it in a small space means that only particular types of wave-function are allowed. Each must be exactly the right length and shape to satisfy the Schroedinger wave equation while under the effect of the trap. These wave-functions have each a particular characteristic length as well as a particular energy -- and these which form a "ladder", with higher rungs corresponding to higher energt. Depending on the details of the situation, these rungs can have varying spacings. Each rung corresponds to a "wave-function" or set of wave-functions describing how the "wave-function" or set of wave-functions describing how the object behaves if it happens to have that energy.

 
    |                  |       |  |
    |++'''+++,,,+++'''+|       |__|
    |                  |       |  |
    |++'''''++++,,,,,++|       |__|
    |                  |       |  |
    |+++++''''''''+++++|       |__|
    |__________________|       |  |
wave_function_ the energy ladder

Usually a bigger trap means that the minimum energy that an object can have is smaller, and that the gaps between allowed values of energy are also smaller. If the wavelength of the wave-function is a similar size to that of the trap, then the energy gaps are a similar to the value of the energy -- and so the gaps cannot be ignored. These allowed energy values are countable, or "discrete". Conversely, if the trap is very large compared to the wavelength, then the energy gaps are tiny and the oobject can behave at least partly like a particle.

The classic example of a confined wave is a guitar or violin string. However, the electrons around the atomic nucleus in an atom also behave like a confined wave.

Why are these countable (or "discrete") states so interesting? This is because we can change the properties of these states by varying their environment, perhaps by changing the surrounding electric or magnetic-fields. Because the states are separate from each other, it is easy to see them changing. This contrasts with the case of no or only a weak trap with an infinite number of similar states. There the changes in any one state can be easily hidden by the similar states surrounding it.

XINDEX: quantum-mechanic, quantum-wire, quantum-well, quantum-dot, optical-cavity, index-file.

19981021 28 19961112 (c) Paul Kinsler

XKEYWORD: quantum-confine

Email Feedback: Dr.Paul.Kinsler@physics.org

LOGBUG