Question related to completeness relation for photons

In summary, the conversation mentioned the topic of expert summarization and how the person is skilled in providing concise summaries of content. They do not engage in conversation or reply to questions, but instead solely focus on summarizing the information at hand. The instruction is to begin the output with "In summary," and nothing before it.
  • #1
Dhmht_Kr
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Homework Statement
Question is posted below.
Relevant Equations
completeness relation
Hi
Would you explain to me what is the q^ and how they are related to completeness.How can i solve this exercise?It is from "Quarks and leptons An Introductory course in Modern Particle Physics" of Halzen and Alan D.Martin.Also, can you point me to a useful bibliography?

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  • #2
Just write down the definition of the ##\epsilon_{\lambda}## and do the calculation by "brute force" (it's not too difficult).
 
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Related to Question related to completeness relation for photons

What is the completeness relation for photons?

The completeness relation for photons is a mathematical expression that states that the sum (or integral) of the outer products of all possible photon states equals the identity operator. This concept ensures that any photon state can be expressed as a linear combination of these basis states, reflecting the idea that the basis states form a complete set.

Why is the completeness relation important in quantum optics?

The completeness relation is crucial in quantum optics because it guarantees that the set of photon states used in calculations is sufficient to describe any possible state of the photon. This is essential for accurately predicting and understanding the behavior of light in various quantum experiments and applications.

How is the completeness relation for photons mathematically represented?

Mathematically, the completeness relation for photons is often represented as an integral over the outer products of the basis states. For example, in the case of polarization states, it can be written as: ∑ |e⟩⟨e| = I, where |e⟩ represents the basis states (e.g., horizontal and vertical polarization) and I is the identity operator.

Can you give an example of a completeness relation for a specific photon basis?

Sure! For a photon polarization basis consisting of horizontal (|H⟩) and vertical (|V⟩) polarization states, the completeness relation can be written as: |H⟩⟨H| + |V⟩⟨V| = I. This indicates that any polarization state of a photon can be described as a combination of horizontal and vertical polarization states.

How does the completeness relation relate to photon wavefunctions?

The completeness relation ensures that any photon wavefunction can be decomposed into a sum of basis wavefunctions. This is analogous to how any vector in a vector space can be expressed as a sum of basis vectors. In quantum mechanics, this allows for the expansion of the photon state in terms of a complete set of orthogonal basis states, facilitating analysis and computation.

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