AT_saavedra
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- Homework Statement
- Please refer to the attached file.
I am trying to make sense of the last part of the "good" states proof.
- Relevant Equations
- Please refer to the attached file.
(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.)
I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of Ψ_{a}^{0} and Ψ_{b}^{0} but right before that the proof just showed that they are orthogonal states. Just from the very basics of linear algebra these two statements seem incompatible to me.
I know there must be some error in my interpretation since the contradiction is too clear not to have been caught by the third version of the book, but despite reviewing the chapter once again, as well as my linear algebra book, I am still completely stuck. If someone could help me get out of this hole I have made for myself, I would deeply appreciate it.
I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of Ψ_{a}^{0} and Ψ_{b}^{0} but right before that the proof just showed that they are orthogonal states. Just from the very basics of linear algebra these two statements seem incompatible to me.
I know there must be some error in my interpretation since the contradiction is too clear not to have been caught by the third version of the book, but despite reviewing the chapter once again, as well as my linear algebra book, I am still completely stuck. If someone could help me get out of this hole I have made for myself, I would deeply appreciate it.