(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two spin-1/2 particles are placed in a system described by Hamiltonian H=S(x1)S(x2), (S(x) being the spin operator in the x-direction). States are written like |[tex]\uparrow\downarrow[/tex]>, (and can be represented by 2 x 2 matrix) so that there are 4 possible states. (|[tex]\uparrow\uparrow>, |\uparrow\downarrow>, |\downarrow\downarrow>, |\downarrow\uparrow>[/tex]

Given: |[tex]\phi> = |\uparrow\downarrow> - |\downarrow\uparrow>[/tex]

Find the normalized eigenstate of |[tex]\phi[/tex]>

2. Relevant equations

S(x1) and S(x2) are both matrices represented by [tex]\hbar[/tex]/2 *

0 1 (I don't know how to write matrices), where x1 operates on the first particle, and x2 on the second.

1 0

3. The attempt at a solution

S(x) inverts the spin, and multiplies the state by [tex]\hbar/2[/tex]; there are 2 spin operators working on the different states so that the whole state in the end will be multiplied by the square of that: [tex]\hbar\stackrel{2}{}/4[/tex].

The difficulty is that I don't understand what is meant by normalized eigenstate. I do end up with a eigenstate (or energy) of -[tex]\hbar\stackrel{2}{}/4[/tex] by calculating <[tex]\phi|\phi>[/tex], but I'm quite sure that's not the definite answer, because something still needs to be normalized.

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# Homework Help: Question concerning Hamiltonian and eigenstates

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