Recent content by ARoyC

Thank you. I need to delve into the proper functional analysis to do this.

I have encountered this problem in Quantum Mechanics. This is my effort. Please pardon my handwriting.

How to prove that the tensor product of two same-dimensional Hilbert spaces is also a Hilbert space? I understand that I need to prove the Cauchy Completeness of the new Hilbert space. I am stuck in the middle.

I am sorry. The screenshots of the questions are directly from MIT OCW. So, I had nothing to do with it.

Few Information: 1. X and Y are written in the {∣0⟩,∣1⟩} X = |0><1| + |1><0| and Y = |0><1| - |1><0| 2. ∣+⟩=(1/√2)*(∣0⟩+∣1⟩)

Update: I studied Engineering for a year, but I found out that it doesn't suit me. Hence, I shifted to Physics. Now I am pursuing Integrated BS-MS (5 Years) in Physics (with a minor in Data Science) at the Indian Institute of Science Education and Research (IISER), Mohali. I have completed my...

I apologise. This is the Pauli Y matrix.

Y is Pauli Y matrix. 0 eigenvalue is common for every linear transformation for (0,0,0). So it is a trivial case. And in these questions, even if they mean that the eigenvalue is 0, then what is the method to do the problems?

Hi, everyone. Please check the following two questions. 1. 2. The questions are from MIT OCW. First of all, I cannot understand what is the meaning of the measurement outcome being 0. How can an eigenvalue be 0? I tried doing the problems guessing that by 0 they mean the posterior state will...

[Mentor Note: Two similar thread starts merged] The questions are from MIT OCW. First of all, I cannot understand what is the meaning of the measurement outcome being 0. How can an eigenvalue be 0? I tried doing the problems guessing that by 0 they mean the posterior state will be |0>. The only...

Oh, okay, thanks a lot!

How are we getting the very first equality that is A = Σ|j><j|A|k><k| ?

Oh! Then we can go to the LHS of the equation from the RHS. Can't we do the reverse?

Hi. I am not being able to understand how we are getting the following spectral decomposition. It would be great if someone can explain it to me. Thank you in advance.

Thank you for the explanation.