- #1
gfd43tg
Gold Member
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I know this is an elementary question, but it has been some time since I multiplied exponentials, and with imaginary terms combined with absolute values, things get muddled up so easy that I want to clear this up
So if I have
$$ \Psi (x,t) = c_{1} \psi_{1} e^{- \frac {i E_{1}}{\hbar} t} + c_{2} \psi_{2} e^{- \frac {i E_{2}}{\hbar} t} $$
I want to find ##\mid \Psi (x,t) \mid^{2}##
Well, I suppose I will do ##\mid \Psi (x,t) \mid \mid \Psi (x,t) \mid##. My first problem is actually determining the absolute value of this quantity.
$$ \mid c_{1} \psi_{1} e^{- \frac {i E_{1}}{\hbar} t} + c_{2} \psi_{2} e^{- \frac {i E_{2}}{\hbar} t} \mid $$
But how to analyze this?
So if I have
$$ \Psi (x,t) = c_{1} \psi_{1} e^{- \frac {i E_{1}}{\hbar} t} + c_{2} \psi_{2} e^{- \frac {i E_{2}}{\hbar} t} $$
I want to find ##\mid \Psi (x,t) \mid^{2}##
Well, I suppose I will do ##\mid \Psi (x,t) \mid \mid \Psi (x,t) \mid##. My first problem is actually determining the absolute value of this quantity.
$$ \mid c_{1} \psi_{1} e^{- \frac {i E_{1}}{\hbar} t} + c_{2} \psi_{2} e^{- \frac {i E_{2}}{\hbar} t} \mid $$
But how to analyze this?