Comments on: Properties of Hermitian Operators

By: catherine therese quiñones

catherine therese quiñones — Fri, 14 Aug 2009 13:35:06 +0000

Hi bebelyn! The way you presented your article is really student friendly. Nice job and keep it up! However, there are things you missed (just minor ones) like putting “det” before the matrix on the first equation of part A and another “det” before the matrix on the second equation of part B. I also have some questions if you don’t mind. I am confused about the degenerate eigenvalues (ie w=3). For w1 you chose x2=0 and x3=1 and for w2 you chose x2=1 and x2=0. What are your basis of choosing the latter values of x2 and x3? Will the result of the Gram-Schmidt be affected if we use other values of x2 and x3? Another thing, In obtaining the trace of the Hermitian matrix, you solved it in two ways right? First is by summing up the diagonal elements and the other is by adding up the eigenvalues. My question is, are these procedures also valid for non-Hermitian matrices? But anyway, thanks for that procedures. It’s amazing that we can also obtain the trace not just by doing diagonalization which is quite long. I hope those techniques are also valid for non-Hermitian matrices.

By: Hananish Joy

Hananish Joy — Tue, 11 Aug 2009 06:35:32 +0000

Thank you for the effort of showing the properties of the hermitian operators in a way that we could understand. I just want to clarify, if we have degenerate states, we need to use Gram Schmidt, right?

Also, the given matrix can not be seen. I think there’s something wrong in the code there.

thanks for making Hermitian matrices simpler to understand.

By: Majvell Kay Odarve

Majvell Kay Odarve — Thu, 06 Aug 2009 04:12:17 +0000

Hello Ms. Bebelyn,

This article is really a great help in my understanding of Hermitian operators. I just have a query on the part where you calculated the eigenvector for the degenerate states. What is the basis for selecting the values of the arbitrary variables x_2 and x_3? Is there any way of directly knowing that the values to be used leads to orthoganal vectors or is it really necessary to perform the Gram Schmidt procedure? Thank you so much and God bless you.

By: Sandra L. Manulat

Sandra L. Manulat — Thu, 06 Aug 2009 04:10:23 +0000

What are the requirements in using the Gram-Schmidt procedure???Is it necessary for all cases of finding the eigenvector???Thank You.

By: Gibson T. Maglasang

Gibson T. Maglasang — Thu, 06 Aug 2009 04:06:16 +0000

Congratulations! For a job well done. I really appreciate it. I fully understand now the concept of hermitian operators and its properties are deeply inculcated in my mind. Two thumbs up to all of you guys.

By: Taylor Series Expansion of Hermitian and Unitary Operators

Taylor Series Expansion of Hermitian and Unitary Operators — Fri, 31 Jul 2009 06:31:23 +0000

[...] the matrix representation of an operator, the procedure in extracting the eigenvalues and corresponding eigenvectors of this operator was [...]

By: bien

bien — Mon, 01 Jun 2009 00:33:48 +0000

There is a missing equation that is very fundamental in your presentation, I guess that was the equation that Simon meant.. Its’very important bebz.

By: jessica

jessica — Fri, 03 Apr 2009 04:48:25 +0000

hello bebelyn,

The article you made is very nice and very comprehensible. Just want to make comment on the alignments of your equations on the latter part for a dandier view.

By: pearl francisco

pearl francisco — Thu, 02 Apr 2009 23:26:06 +0000

Hi bebelyn, I must say that it is indeed a nice article. The presentation of the properties of hermitian operators are clearly stated.

By: Cariel

Cariel — Wed, 01 Apr 2009 13:20:53 +0000

Hi Bebelyn. You have done a nice job about the Properties of Hermitian Operators. It is very detailed. I am just confused of the notation you are using on the adjoint of the unitary matrix. Can it be changed?