Annihilation vs. Creation Operators: What's the Difference?

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Discussion Overview

The discussion centers on the differences between annihilation and creation operators in quantum mechanics, specifically regarding their eigenstates and the implications of these differences. Participants explore the theoretical aspects of these operators and their definitions within the context of coherent states.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant states that coherent states are defined as eigenstates of the annihilation operator, questioning whether this is merely a convention or if there is a deeper reason behind it.
  • Another participant asserts that there are no eigenstates of the creation operator and suggests that the asymmetry between the two operators arises from the nature of the ordered basis, which includes a first element but lacks a last element.
  • A participant reiterates the question about the essential difference between the eigenstates of the annihilation and creation operators, emphasizing the concept of existence.

Areas of Agreement / Disagreement

Participants express differing views on the existence of eigenstates for the creation operator, indicating a lack of consensus on the fundamental differences between the two types of operators.

Contextual Notes

The discussion does not resolve the implications of the asymmetry mentioned, nor does it clarify the definitions or assumptions regarding the eigenstates of the operators.

gerald V
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Cohererent states are defined as eigenstates of the annihilation operator. Never the creation operator is referred to.

Is this just a convention or is more behind? What is the essential difference between eigenstates of the annihilation- versus the creation operator?

Thank you very much in advance!
 
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There are no eigenstates of the creation operator. The asymmetry between creation and annihilation operators stems from the fact that the ordered basis ##\{|0\rangle, |1\rangle, |2\rangle,\ldots\}## has the first element but not last element.
 
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gerald V said:
What is the essential difference between eigenstates of the annihilation- versus the creation operator?

Existence!
 
Got it. Thank you very much.
 

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