Crucial step Quantum mechanics

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Discussion Overview

The discussion revolves around a specific step in quantum mechanics related to calculating the van der Waals forces between two hydrogen atoms in the ground state. Participants are seeking clarification on a mathematical transition between two equations presented in an attached file.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the transition from equation (19) to (20) in the context of quantum mechanics.
  • Another participant suggests that the question pertains to an advanced topic and indicates they cannot assist.
  • A different participant proposes that the transition is straightforward and references the completeness relation in quantum mechanics, suggesting it leads to the result .
  • One participant acknowledges the previous response but requests further explanation on a specific relation involving the summation of terms.
  • Another participant relates the mathematical expression to a known algebraic identity, indicating a connection to the original query.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the clarity of the transition between the equations, as some find it straightforward while others express confusion and seek further clarification.

Contextual Notes

The discussion includes assumptions about the completeness relation and the mathematical properties of quantum states, which may not be fully articulated by all participants.

Gavroy
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hi

i am just doing some quantum mechanics. unfortunately, i have spent the last 2 hours on one single step, which i do not understand at all.

i don't get it, how you get from (19) to (20) in the attached file?

could somebody explain this to me?
 

Attachments

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It might help people in deciding whether to download the PDF, to know that your question is about a fairly advanced topic: calculating the van der Waals forces between two hydrogen atoms in the ground state.

(Unfortunately I can't help.)
 
Isn't it just straightforward? If there's something subtle, I'm missing it too.

Σi |<Bi|Q|A>|2 = Σi <A|Q| Bi><Bi|Q|A>

Completeness says Σi |Bi><Bi| = I

so the result is <A|Q2|A>
 
oh ya...thanks
 
sorry, I overlooked something:
Bill_K said:
Σi |<Bi|Q|A>|2 = Σi <A|Q| Bi><Bi|Q|A>
could you explain this relation to me?
 
Last edited:
Well, you know that in algebra [itex]z z^{*} = |z|^2[/itex], right ? Now pick [itex]z= \langle A|Q|B_i\rangle[/itex].
 
:wink: okay...i got it...thanks
 

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