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Question: Can I define the creation and annihilation operator commutation relations with an explicit momentum dependence?

Question:Can I define the creation and annihilation operator commutation relations with an explicit momentum dependence?

nmacsai 260 Maple 2024
physics momentum annihilation
March 02 2025
1

Can I define the creation and annihilation operator commutation relations with an explicit momentum dependence?

The goal is to implement an expression of a discrete scalar plane-wave solution to the Klein-Gordon equation that makes use of the creation and annihilation operators in the Physics package.

We don't bother solving the Klein-Gordon equation explicitly. Instead, we just take a solution from literature. This approach is sufficient to show the difficulty in defining the the creation and annihilation operators in this way.

how_to_define_creation_and_annihilation_operators_with_a_momentum_dependence.mw

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Setup

   

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Goal

   

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Define Creation and Annihilation Operators for Quantum Field phi

   

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Static Textbook Solution

   

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Commutator Definition Attempt 1 FAIL

   

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Commutator Definition Attempt 2 FAIL

   

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Commutator Definition Attempt 3 FAIL

   

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Commutator Definition Attempt 4 FAIL

   

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Commutator Definition Attempt 5 FAIL

   

So, is defining the creation and annihilation operators with a momentum dependence even possible, using the physics MAPLE package?

Download how_to_define_creation_and_annihilation_operators_with_a_momentum_dependence.mw
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