Wavelength in QM: Definition & Measurement

[suku]

Can anyone tell me how is wavelength defined for a wave associated with a particle?
If the wave function we are speaking of has no physical significance,then how can measure its length?
tks for any rpl

 

[muppet]

By "wavelength" in QM one usually means the de Broglie wavelength, defined by
$$\lambda=\frac{h}{p}$$
where p is the momentum of a particle and h is Planck's constant.

The wavefunction is neither physically insignificant nor something you measure directly. For a basic introduction to what the wavefunction means, see the library article on wave-particle duality; for a more technical description see that on wave function.

 

[Entropia]

In quantum mechanics, a wave associated with a particle is described by its wave function, which is a mathematical representation of the probability amplitude of the particle's position in space and time. The wavelength of this wave function is defined as the distance between two adjacent peaks or troughs in the wave. However, it is important to note that this wavelength is not a physical property of the particle itself, but rather a mathematical description of its behavior.

As for how we can measure the wavelength of a particle's associated wave, this is done through experiments and observations. For example, in the double-slit experiment, the interference pattern created by a particle passing through two slits can be used to determine its wavelength. Additionally, techniques such as diffraction and spectroscopy can also be used to measure the wavelength of particles.

It is true that the wave function itself may not have physical significance, as it is a mathematical construct. However, it is a crucial tool in understanding the behavior of particles in quantum mechanics and has been extensively tested and confirmed through experiments. Therefore, while we may not be able to physically measure the length of a wave function, we can still use it to make predictions and understand the behavior of particles in the quantum world.