Single electron wave packet in Fock space?

In summary, constructing a state that closely corresponds to the idea of a single electron wave packet as a superposition of Fock states is possible by setting all Fock states except for N=1 to zero. This can be done by representing the Fock states in momentum and choosing only the 1-particle sector. However, this may not be compatible with the QFT formalism.
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MisterX
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How might we construct a state most closely corresponding to the idea of a single electron wave packet as some superposition of Fock states?
 
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  • #2
MisterX said:
How might we construct a state most closely corresponding to the idea of a single electron wave packet as some superposition of Fock states?

I don't think that's compatible with the QFT formalism of a superposition of 0 particle, 1 particle, 2 particle states etc - but someone who knows more than I do may have an answer - I certainly don't. A wave-packet is of a single particle.

Thanks
Bill
 
  • #3
It is a pure Fock state in its 1-particle sector. A general Fock state has the form $$\psi=\psi_0+\psi_1+\psi_2+\ldots$$ of a superposition of N-particle states \psi_N. In a momentum representation the latter are of the form $$\psi_N=\int dp_1...dp_N \psi_N(p_1,\ldots,p_N)|p_1,\ldots,p_n\rangle$$. Now put all \psi_N to zero except for N=1, and you can translate your wave packet exactly into a state in Fock space.
 
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Related to Single electron wave packet in Fock space?

1. What is a single electron wave packet in Fock space?

A single electron wave packet in Fock space is a mathematical representation of the quantum state of a single electron in a system. It describes the probability distribution of the electron's position and momentum in a specific region of space and time.

2. How is a single electron wave packet in Fock space different from a classical wave packet?

A single electron wave packet in Fock space is fundamentally different from a classical wave packet because it takes into account the probabilistic nature of quantum mechanics. Unlike a classical wave packet, the position and momentum of the electron in a single electron wave packet cannot be known with certainty.

3. What is the significance of studying single electron wave packets in Fock space?

Studying single electron wave packets in Fock space is important for understanding the behavior of electrons in quantum systems. It allows us to make predictions about the properties and interactions of electrons, which is crucial for the development of new technologies such as quantum computers.

4. How is a single electron wave packet created in Fock space?

A single electron wave packet can be created in Fock space through a process called wave function collapse. This occurs when an observation or measurement is made on the electron, causing its wave function to collapse into a single state.

5. What are some real-world applications of single electron wave packets in Fock space?

Single electron wave packets in Fock space have potential applications in a variety of fields, including quantum computing, quantum cryptography, and quantum metrology. They could also be used in the development of more efficient and precise electronic devices.

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