Debroglie Wavelength: Trapped Particle's Lamda=2L/n

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Start date Oct 27, 2005
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Debroglie Debroglie wavelength Wavelength

In summary, Debroglie Wavelength, also known as matter wave, is the wavelength associated with a moving particle and is defined as the ratio of Planck's constant to the momentum of the particle. It can be calculated for a trapped particle using the formula lambda=2L/n, where L is the length of the trap and n is the quantum number associated with the particle's energy state. The Debroglie Wavelength plays a crucial role in quantum mechanics by explaining the wave-particle duality of matter. It has been observed in various experiments and affects the movement of particles by determining their momentum and position uncertainty, as described by the Heisenberg uncertainty principle.

Oct 27, 2005

asdf1

why is the debroglie wavelength of a trapped particle equal to lamda=2L/n?

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Oct 27, 2005

Galileo

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Because of the boundary conditions. The wavefunction will be a standing wave with nodes at the boundary, like a vibrating string fixed at both ends.

Oct 28, 2005

asdf1

thanks! :)

What is Debroglie Wavelength?

Debroglie Wavelength, also known as matter wave, is the wavelength associated with a moving particle, proposed by French physicist Louis Debroglie. It is defined as the ratio of Planck's constant to the momentum of the particle.

How is Debroglie Wavelength calculated for a trapped particle?

The Debroglie Wavelength for a trapped particle is given by the formula lambda=2L/n, where L is the length of the trap and n is the quantum number associated with the particle's energy state.

What is the significance of Debroglie Wavelength in quantum mechanics?

The Debroglie Wavelength plays a crucial role in quantum mechanics as it relates to the wave-particle duality of matter. It helps explain the behavior of particles at the quantum level, where they exhibit both wave-like and particle-like properties.

Can the Debroglie Wavelength be observed in experiments?

Yes, the Debroglie Wavelength has been observed in various experiments, such as the double-slit experiment, where particles behave like waves and interfere with each other. It is also used in electron microscopy to determine the resolution of images.

How does the Debroglie Wavelength affect the movement of particles?

The Debroglie Wavelength affects the movement of particles by determining their momentum and position uncertainty. As the wavelength decreases, the momentum and position uncertainty increase, making it more difficult to predict the exact location of the particle. This is a fundamental principle of quantum mechanics known as the Heisenberg uncertainty principle.