This applet illustrates Heisenberg's (position-momentum) Uncertainty Principle in quantum mechanics.

The user specifies a momentum spectrum and the applet plots the corresponding spatial probability density (position spectrum), as well as the real and imaginary parts of the wavefunction. The user can choose (continuous) gaussian or square spectra with variable central momentum and width. Alternatively, the user can construct an arbitrary discrete spectrum.

If the momentum spectrum is peaked around a particular value, then so is the spatial probability density. If the width of the momentum spectrum is small, then that of the position spectrum is large, and vice versa. This is Heisenberg's (position-momentum) Uncertainty Principle.

The mathematical expression of the Uncertainty Principle is that the product of the two widths is always greater than a minimum value which is about the size of Planck's constant:

- The coefficients in the momentum spectrum are restricted to be real in the applet.
- The applet uses units in which Planck's constant is 1.
- In the demo version, the real and imaginary parts of the wavefunction are not plotted, and the square momentum distribution is not available.

**Instructions for use**

- Continuous distributions:
- Using the popup menu, choose the type of continuous distribution desired.
- Adjust the central momentum and width using the scrollbars provided.

- Discrete distributions:
- Choose "user-defined" on the popup menu.
- Build up a momentum distribution by clicking (several times) in the right-hand plane.
- To start again, click "clear".