Matrix formulation of an operator

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Homework Help Overview

The discussion revolves around the matrix formulation of an operator R acting on an N-dimensional linear vector space spanned by ortho-normal basis states. The original poster expresses difficulty in obtaining the expected results when applying the operator R to the basis vectors, specifically noting discrepancies in the outcomes compared to the defined behavior of the operator.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the matrix representation of the operator R and its application to basis vectors. Questions arise regarding the correctness of the matrix entries and the expected results when operating on specific basis states. There is also discussion about the implications of the matrix structure and its relation to the operator's defined behavior.

Discussion Status

The discussion is ongoing, with various participants attempting to clarify the matrix representation and its application. Some have offered insights into potential errors in understanding the operator's action, while others are questioning specific entries in the matrix and their implications. There is a recognition of confusion regarding the relationship between matrix elements and basis vectors.

Contextual Notes

Participants are working under the constraints of the problem statement, which defines the operator's action on the basis states. There is an acknowledgment of potential misunderstandings regarding matrix multiplication and the representation of basis vectors.

  • #31
tanaygupta2000 said:
Sir please assist me where am I doing mistake.View attachment 278400
That's simply wrong. I can't imagine what process you're using for matrix multiplication of a vector, but it's not the right one.
 
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  • #32
tanaygupta2000 said:
I just tried using a hermitian of R since it is behaving like a rotation matrix and I got ... is this good?View attachment 278403
You're matrix multiplication is correct, but you have the wrong idea about what a basis vector is.
 
  • #33
PeroK said:
You're matrix multiplication is correct, but you have the wrong idea about what a basis vector is.
You told it is b1> = transpose(1, 0, 0, ...,)
 
  • #34
tanaygupta2000 said:
You told it is b1> = transpose(1, 0, 0, ...,)
Which is right. You're confusing it with the first component of a vector.
 
  • #35
PS The root of your problem is that you haven't mastered matrices and vectors. You have basic errors and confusions.
 

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