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I have read about de Broglie hypothesis that matter like light can also exhibit wave particle duality. This gave rise to the following questions in my mind.

  1. The wavelength for electrons is significant. So does that mean that electrons are both particles and waves at the same time or they show different behaviour in different experiments. Or they are only waves.

  2. I cannot understand why only moving objects will possess a wavelength.

  3. What kind of waves will electrons be like light is an electromagnetic wave.

  4. If electrons behave like waves then will the electric current flowing in wires also be considered as waves.

Please provide me the explanation. Thank you very much

Qmechanic
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Ashok Sharma
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1 Answers1

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de Broglie hypothesis is a historically significant development that has very little bearing on what is happening now. IMHO it is only relevant for historians.

  1. Electrons behave like quantum particles with wavefunction (or a more abstract state vector in Hilbert space) governed by Schrodinger equation (other equivalent formalisms exist). They are neither waves, nor particles. Historically, people talked about wave-particle duality, but this concept does not help you to solve the propblem, neither does it help conceptually. Most of the time it simply confuses.

  2. Not all particles in QM can be given a definite wavelength. Definite wavelength is only possible if the particle is strongly de-localized. Lets say you have a particle described by wavefunction $\psi\left(\mathbf{r},\,t\right)$. One extreme is then that location of particle is precise, i.e. point in space and time. Another extreme is that location of particle is nearly arbitrary, so probability of finding the particle is $\left|\psi\left(\mathbf{r},\, t\right)\right|^2=const$ for all positions $\mathbf{r}$. Basic maths, coupled with translational invariance of free space then tell you that $\psi\left(\mathbf{r},\, t\right)\propto\exp\left(i\mathbf{k}.\mathbf{r}\right)$, for some vector $\mathbf{k}$. Wavelength is then $\lambda_{Broglie}=2\pi/\left|\mathbf{k}\right|$. Wether particle is (inertially) moving or not does not change this logic (but does have stipulations for the value of $\mathbf{k}$)

  3. Makes no sense. I think you left out some words.

  4. Sort of. There are a lot of complications there due to impurities and thermal noise. The closest to this simple picture are superconductors. There, indeed, within Ginzburg-Landau treatment, one can describe the current flow with a collective wave-function for all electrons (current then is an operator that you apply to the wavefunction).

Cryo
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