(adsbygoogle = window.adsbygoogle || []).push({}); URGENT: QM Series Representation of Bras, Dirac Brackets

1. The problem statement, all variables and given/known data

Suppose the kets |n> form a complete orthonormal set. Let |s> and |s'> be two arbitrary kets, with representation

|s> = [tex]\sum c_n|n>[/tex]

|s'> = [tex]\sum c'_n|n>[/tex]

Let A be the operator

A = |s'><s|

a) Give the series representation of the bras <s| and <s'|.

b) Express [tex]c_n and c'_n[/tex] in terms of Dirac brackets.

c) Calculate in terms of Dirac brackets the matrix elements of A[tex]^+[/tex], the Hermitian conjugate of A.

2. Relevant equations

3. The attempt at a solution

a) I know that the bras corresponding to the kets are row vectors where we take the complex conjugate of each element. That's all I've got.

b) c_n = <s|n> and c'_n = <s'|n>

Of course to go any further, I need the answer to part a.

c)To find the matrix elements of A (NOT [tex]A^+[/tex], I don't know how to do that exactly) we do the following for the element in row m, column n:

[tex]A_{mn}[/tex] = <m|s'><s|n>

What is the Hermitian conjugate of A so that I can use the same method? Once I know the matrix for A+, can I tell if A is Hermitian without finding the matrix for A?

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# Homework Help: : QM Series Representation of Bras, Dirac Brackets

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