Wave in particle in 1 box with infinite potential energy

In summary, a "wave in particle in 1 box with infinite potential energy" is a theoretical model used in quantum mechanics to describe the behavior of a particle constrained to a one-dimensional space with infinitely high potential barriers. This model helps us understand the wave-particle duality of particles and predict their behavior in confined spaces. While not directly applicable to real-world systems, it can be used as a foundation for more complex models. As the potential energy is varied, the particle's energy levels and wave function also change, resulting in a more confined or free-moving particle.
  • #1
td21
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Homework Statement


Q.1Why when the particle's kinetic energy is smaller, the wave has longer wavelength and higher amplitude?
Q.2 Why the length of box decrease in ground state?

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Homework Equations





The Attempt at a Solution


Q.1 wavenumber [itex] k= \frac{\sqrt{2m(U-E)}}{\hbar} [/itex], isn't it?
so KE decreases, wavenumber decreases, wavelength increases?
But isn't the amplitude just (2/L)^(1/2), from the normalization techinque?

Q.2 I really do not know why the box suddenly "contract" in the ground state.
 

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  • #2
can someone tell me why the amplitude of wave is affected by kinetic energy(E-U)?
 

1. What is a "wave in particle in 1 box with infinite potential energy?"

A "wave in particle in 1 box with infinite potential energy" is a theoretical model used in quantum mechanics to describe the behavior of a particle confined to a one-dimensional space with an infinitely high potential barrier at either end. This model can help us understand the wave-like nature of particles and their energy levels.

2. How does the potential energy affect the behavior of the particle in this model?

The infinite potential energy barriers at each end of the box act as a constraint on the particle, limiting its movement within the box. This leads to the particle exhibiting wave-like behavior, with its energy levels being quantized and only certain wavelengths being allowed.

3. What is the significance of this model in quantum mechanics?

This model helps us understand the wave-particle duality of particles, where they can exhibit both wave-like and particle-like behavior. It also allows us to predict and analyze the energy levels and behavior of particles in confined spaces, which has important applications in fields such as nanotechnology and materials science.

4. Can this model be applied to real-world systems?

While the concept of a particle in a box with infinite potential energy is a simplification and not directly applicable to real-world systems, it can be used as a building block for more complex models that can accurately describe the behavior of particles in confined spaces.

5. How does the wave function of the particle change as the potential energy is varied?

As the potential energy of the particle in the box is varied, the allowed energy levels and corresponding wave functions also change. When the potential energy is increased, the energy levels become more closely spaced and the wave function becomes more localized, leading to a more confined particle. When the potential energy is decreased, the energy levels become more spread out and the wave function becomes more spread out, allowing the particle to move more freely within the box.

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