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According to my understanding of QC/QM:

  1. A matrix is a function/operation which when applied on vectors, changes/rotates them.
  2. Ket and bra notation is used to denote quantum state.

Question 1: <0|0> gives scalar

when bra zero and ket zero are multiplied we get a scalar. I understood this numerically but what exactly is this scalar? what does it represent?

Question 2: |0><0| gives matrix

when ket zero and bra zero is multiplied we get a matrix, I understood it numerically but what exactly this matrix represent?

Bonus Question:

since bra and ket represent quantum states so multiplying two quantum states give a scalar or matrix. what does it mean to multiply quantum states? why do we multiply quantum states? Like multiplying a scalar with vector SCALES the vector, here role of multiplication is easy to get.

Vinay Sharma
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    each post should contain a single, laser-focused question. Please feel free to edit the post accordingly. You can ask different questions on different posts – glS May 12 '22 at 09:10
  • @gIS, okay I will do that – Vinay Sharma May 12 '22 at 09:44
  • @TristanNemoz, thanks for input, I couldn't understand at my first reading of suggested link but now it seems similar, please mark duplicate. – Vinay Sharma May 12 '22 at 11:07

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