# How do the wave properties of an electron change with its motion?

How do the wave properties of an electron change with its motion? What about when it is stationary?

• "stationary" is an ambiguous word. An electron may be at rest. The typical terminology in QM uses the word stationary for the state of the quantum object, e.g. stationary state. In a stationary state the electron is not at rest. For instance in the ground state in an atom the electron has a nonzero kinetic energy. Mar 22, 2017 at 20:04

Does a stationary electron exhibit wave-particle duality?

Yes, the electron has a DeBroglie Wave frequency, where $E=hf$,

$E$ being the total relativistic energy, so just the rest mass energy if the electron is at rest.

If so, how do its wave properties change with its motion?

The energy and frequency will be greater the faster the electron moves.

$E = \frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}$, where $m$ is rest mass.

• Can you be more specific about how its energy and frequency are related to its velocity? May 5, 2014 at 21:05
• yes, I added to the answer May 5, 2014 at 21:56
• I wouldn't include relativity here: if you talk about de Broglie wave, you are in non-relativistic regime, otherwise you must speak about bispinor wavefunction instead. Jul 12, 2014 at 15:48
• one should stress that the wave is a PROBABILITY wave, the probability of measuring an electron in a specific x,y,z is a distribution that displays wave properties. Sep 14, 2014 at 3:00
• @annav I disagree with the interpretation that the wave-function describing the dynamics the electron is a PROBABILITY wave. People legitimely ask whether the wave-function is a REAL thing. We don't know enough, for the moment, for answering in the positive or in the negative to this question. Another issue: the terminology "probability wave" is not exact. The wave-function comprises amplitudes of probability, endowed with phases. This is what brings similarity between QM and wave machanics (of course, there are also differences between QM and classical wave mechanics). Mar 20, 2017 at 23:13