De Broglie wavelength in non-constant potential?

In summary, the de Broglie wavelength can have significance for the wavefunctions of particles in a non-constant potential. This can be seen in the energy eigenstates of the quantum harmonic oscillator, where the wavelength varies with position. This has implications for diffraction, the double-slit-behaviour of electrons, and the energy levels of a particle in a box.
  • #1
greypilgrim
515
36
Hi.

Does the de Broglie wavelength have any significance for the wavefunctions of particles in a potential that is non-constant in no region of space? As far as I can see, the solutions of the time-independent Schrödinger equation are only sinusoidal if ##E>V=const##.

This is enough to derive diffraction and the double-slit-behaviour of electrons and even the energy levels of a particle in a box "the old q.m. way", i.e. without the Schrödinger equation. But is it relevant in a wider context?
 
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  • #2
If a particle's potential energy varies with position, then so does its kinetic energy, in order to keep the total energy constant. If the kinetic energy varies with position, then so do the momentum and the wavelength. You can see this in the energy eigenstates for the quantum harmonic oscillator: the wavelength is longer at locations further from the center.
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(from Wikipedia)
 

1. What is the De Broglie wavelength in non-constant potential?

The De Broglie wavelength in non-constant potential refers to the wavelength associated with a particle moving through a varying potential field. It is a fundamental concept in quantum mechanics and is related to the momentum and energy of the particle.

2. How is the De Broglie wavelength affected by non-constant potential?

In non-constant potential, the De Broglie wavelength is affected by the changes in the potential energy of the particle. As the particle moves through regions of different potential, its wavelength will change accordingly.

3. What is the significance of the De Broglie wavelength in non-constant potential?

The De Broglie wavelength in non-constant potential is significant because it helps us understand the wave-particle duality of matter. It demonstrates that particles such as electrons can exhibit wave-like properties, and their behavior is not solely described by classical mechanics.

4. How is the De Broglie wavelength calculated in non-constant potential?

The De Broglie wavelength in non-constant potential is calculated using the formula λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. In non-constant potential, the momentum is a function of the potential energy, so the wavelength will vary accordingly.

5. What are some real-world applications of the De Broglie wavelength in non-constant potential?

The De Broglie wavelength in non-constant potential has various applications in fields such as quantum mechanics, solid-state physics, and electron microscopy. It is also used in the development of technologies such as electron microscopes, particle accelerators, and quantum computing.

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