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I'm new to matrix mechanics in quantum mechanics and I admit that linear algebra is the weakest part of my maths toolkit but I have an operator to convert to matrix form. I'm about 85% sure I've done it right, however I can't solve for the eigenvectors. I'm sure I'm missing something obvious and was wondering if someone could help me find it.

The operator is a Hamiltonian of the form.

[tex] H=c \left[ \begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array} \right] [/tex]

If I solve for the eigenvalues I get [itex] \lambda = \pm c [/itex]

Which seems right. However, if I try to solves for the eigenvectors using [itex] H'=(H-\lambda I) [/itex] and [itex]H'x = 0 [/itex] for the eigenvalue +c, I get a set of equations that don't make sense to me.

[tex]H'=c \left[ \begin{array}{cc} 1-1 & 1 \\ 1 & -1-1 \end{array} \right]= \left[ \begin{array}{cc} 0 & 1 \\ 1 & -2 \end{array} \right] [/tex]

Using x=(x,y), and if I'm reading this right, this would give a set of equations where y=0 but also y=x. This would imply the answer is a null vector which makes no sense.

Can anyone see where I've gone wrong/what I'm missing?

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# Homework Help: Urgent: Confusing matrix operator equation

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