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Calculating eigenstates of an operator
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[QUOTE="barefeet, post: 4997958, member: 490981"] I see, but I still get one non trivial solution out of it. If one is 0, then both are 0. So they are either both nonzero or both 0. If they are nonzero, I can write: [tex] a_n = \frac{c_1 + c_2}{c_1} = \frac{c_1 + c_2}{c_2} [/tex] If [itex] c_1 + c_2 =0 [/itex] then [itex] a_n =0 [/itex] or the c's are 0. If [itex] c_1 + c_2 [/itex] is nonzero, then I can divide by it and gives me [itex] c_1 = c_2 [/itex] with [itex] a_n = 2 [/itex] Unnormalized I can take as eigenstate [itex] \mid \alpha \rangle + \mid \beta \rangle [/itex]. Now I can't find the other eigenstate. [itex] \mid \alpha \rangle - \mid \beta \rangle [/itex] is orthogonal to this eigenstate but letting A operate on it gives me 0. Or does this just mean that it is an eigenstate with eigenvalue 0? [/QUOTE]
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Calculating eigenstates of an operator
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