Localized High Energy Particle in a Box: Examining Superposition Limits

In summary, the conversation discusses the possibility of writing down the wave function of a localized high energy particle in a large box, using a superposition of momentum eigenstates. It is noted that this is possible through a Fourier transform, but throwing away any number of eigenstates may not result in the correct solution. The practical implications of this vary depending on the situation.
  • #1
Spinnor
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Say we do physics in a very large box of side L. Using the proper superposition of a countable number of momentum eigen states can we write down the wave function of a localized high energy particle in a box?

If so, assume the number of superposed momentum states is N. Now randomly throw away half the N momentum states. Is the resultant superposition still nearly a localized high energy particle? How much can be thrown away, if any, and still have a pretty good Gaussian? If I have a superposition of a trillion momentum eigen states and I throw away one what harm did I do?

Thanks for any help!
 
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  • #2
Spinnor said:
Say we do physics in a very large box of side L. Using the proper superposition of a countable number of momentum eigen states can we write down the wave function of a localized high energy particle in a box?

They are eigenstates of energy - not momentum.

But by means of a Fourier transform you can go to the momentum representation - but you have just changed the representation - not the fact you have countable eigenstates:
http://en.wikipedia.org/wiki/Particle_in_a_box

If you throw away any - one - a million - it doesn't matter - its not the correct solution. Practically - well that depends on the situation.

Thanks
Bill
 
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FAQ: Localized High Energy Particle in a Box: Examining Superposition Limits

What is a localized high energy particle in a box?

A localized high energy particle in a box is a theoretical concept in quantum mechanics where a particle is confined within a specific region, known as a "box", and has a high amount of energy. This is often used to study the behavior of particles in a controlled environment.

How is superposition limited in this scenario?

In this scenario, superposition is limited because the particle is confined to a specific region or "box". This means that its wave function cannot spread out and exist in multiple places simultaneously, as is typically seen in quantum mechanics. Instead, the particle's wave function is forced to collapse and exist in a single location within the box.

What are the practical applications of studying localized high energy particles in a box?

Studying localized high energy particles in a box can help scientists better understand the behavior of particles in controlled environments, which can have practical applications in fields such as quantum computing and particle physics. It can also provide insights into the fundamental principles of quantum mechanics and the nature of matter.

How does this concept relate to the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. In the case of a localized high energy particle in a box, the particle's position is confined to a specific region, which means that its momentum is less certain. This principle is fundamental to quantum mechanics and is often observed in experiments involving confined particles.

Are there any limitations to this theoretical concept?

Like all theoretical concepts, there are limitations to the model of a localized high energy particle in a box. It is a simplified representation of a complex phenomenon and does not take into account factors such as external forces and interactions with other particles. Additionally, it is a purely theoretical concept and has not been directly observed in experiments. However, it serves as a useful tool for studying the behavior of particles in controlled environments and gaining a deeper understanding of quantum mechanics.

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