## 3 Badges

4 years, 174 days

## @ecterrab  Thank you very much for...

Thank you very much for your thorough answer! I guess I have to live with checking the summation indices manually.

## @ecterrab  Thanks for the help. Re...

Thanks for the help. Regarding issue 2: I understand, but is there no way to do that automatically? Even the expression

Projector(Ket(A, i))-Projector(Ket(A, j))

is not evaluated to 0, although j is just another dummy index. Since the dummy indices change automatically when working with projections onto projectors, it is quite an effort to look at all the dummy indices in a long expression. For example, in

Projector(Ket(A, i)) . Ket(B, i)


the "i" in the projector is changed to "i_1" to avoid index collisions.

## @ecterrab Again, thank you very muc...

Again, thank you very much for the help. Yes, when I try to edit the procedure, the lower left box in maple changes from "Ready" to "Evaluating..." and then maple aborts while consuming all of the memory my laptop has.  I will just aoivd touching the procedure.

Edit. Same hapens when I just mark and try to copy the procedure in the worksheet from your last post. At least, after the kernel aborts, I can still edit the document, save it and restart maple.

## @ecterrab  Thank you for the hints...

Thank you for the hints. Unfortunately, whenerver I want to edit the procedure (replacing op(2, K) with op(2..-1, K)) maple consumes all of the memory (16GB) and aborts with the error "Kernel connection lost".

## @ecterrab Thanks for this nice solu...

Thanks for this nice solution. Unfortunately, it is a bit buggy (see attachment). In any case, this will hopefully suffice for now.

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This works nicely

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This is buggy

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However, this here works, I guess due to the bracketrules above

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But there are also problems when Bra/Ket is a state whose space is not specified

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Another problem: Other symbols than kets in front of H:

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Workaround

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Download algebra_rules_(reviewed_II)_bugs.mw

## @ecterrab  Hi, thank you very muc...

Hi,

thank you very much for your thorough reply. I apologize for this late answer. For some reasons, I did not get a notification that someone answered.

Your answer was exactly what I needed. However, I have two remaining questions:

- You use F as a continuous basis. What I wanted to achieve with "t" is actually a t-dependence of the basis states ( Bra(A,i) ) and so on. ( t is time and the basis is time-dependent). I guess I can do this also with an auxiliary continuous Hilbert space as you have done with F. Is this the preferred way?

- How to specify matrix elements for operators  with this approach? See below for an explanation. The Hermitian operator "H" should act on the space C = A \otimes B.

Best regards,

Henrik

 (1)

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This works

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This does not work

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What I want

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Download twoD_matrixElements.mw

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