- #1
kq6up
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If I define a state ket in the traditional way, Say:
$$|\Psi \rangle =\sum _{ i }^{ }{ a_{ i }|\varphi _{ i }\rangle \quad } $$
Where $$a_i$$ is the probability amplitude.
How does:
$$\hat {H } |\Psi \rangle =E|\Psi \rangle $$ if the states of $$\Psi$$ could possibly represent states that have different energy levels, and one would not be able to factor the energy eigenvalue out of the summation. I know I am missing something big here. Could someone point it out?
Edit: Does $$ \hat {H} $$ collapse psi to one state phi, and so render only energy eigenvalue of the one phi that remains?
Thanks,
Chris Maness
$$|\Psi \rangle =\sum _{ i }^{ }{ a_{ i }|\varphi _{ i }\rangle \quad } $$
Where $$a_i$$ is the probability amplitude.
How does:
$$\hat {H } |\Psi \rangle =E|\Psi \rangle $$ if the states of $$\Psi$$ could possibly represent states that have different energy levels, and one would not be able to factor the energy eigenvalue out of the summation. I know I am missing something big here. Could someone point it out?
Edit: Does $$ \hat {H} $$ collapse psi to one state phi, and so render only energy eigenvalue of the one phi that remains?
Thanks,
Chris Maness
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