Question

What is the de Broglie theorem?

Answer 1

The de Broglie theorem, proposed by French physicist Louis de Broglie in 1924, suggests that particles, like electrons, not only have properties of matter (such as mass) but also exhibit properties of waves. This was a major breakthrough in quantum mechanics.

According to de Broglie, every moving particle can be associated with a wave, called the de Broglie wave, and this wave has a wavelength (\( \lambda \)) given by the formula:

\[
\lambda = \frac{h}{p}
\]

Where:

1. \( \lambda \) is the wavelength of the particle,
   

1. \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J·s} \)),
   

1. \( p \) is the momentum of the particle, which is the product of its mass (\( m \)) and velocity (\( v \)): \( p = mv \).
   

This wave-particle duality means that, depending on the context, particles can behave like both waves and particles. For large objects like cars or baseballs, their wavelength is so small that we don't notice wave-like behavior. But for very small particles, like electrons, the wave behavior becomes significant and can explain phenomena like electron diffraction (which is the bending of waves when they pass through small openings).

In essence, de Broglie's theorem helped to bridge the gap between classical and quantum physics by suggesting that everything that moves behaves like both a particle and a wave to some extent.