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[SOLVED] Superposition of two wavefunctions
The problem is more of complex number arithmetic more then conceptual :
![Printed notes on the superposition principle: if psi1 and psi2 are wave functions, a linear combination psi = c1 psi1 + c2 psi2 is also a wave function; with psi1 = |psi1|e^(i alpha1) and psi2 = |psi2|e^(i alpha2), |psi|^2 expands to include 2Re{c1 c2* psi1 psi2* exp[i(alpha1 - alpha2)]}, labelled as interference from phase difference.](https://www.physicsforums.com/attachments/superposition-jpg.44717/ "Superposition.jpg")
[itex]|\psi|^{2}=\psi\psi^{*}[/itex]
I simply used the equation given above, but instead of getting 2Re{...} I get :
[itex]|\psi_{1}||\psi_{2}| \left( c_{1}c_{2}^{*}\exp({i(\alpha_{1}-\alpha_{2})})+c_{1}^{*}c_{2}\exp({-i(\alpha_{1}-\alpha_{2})})\right)[/itex]
Could someone explain how is this equal to that given in the notes I attached ?
Homework Statement
The problem is more of complex number arithmetic more then conceptual :
Homework Equations
[itex]|\psi|^{2}=\psi\psi^{*}[/itex]
The Attempt at a Solution
I simply used the equation given above, but instead of getting 2Re{...} I get :
[itex]|\psi_{1}||\psi_{2}| \left( c_{1}c_{2}^{*}\exp({i(\alpha_{1}-\alpha_{2})})+c_{1}^{*}c_{2}\exp({-i(\alpha_{1}-\alpha_{2})})\right)[/itex]
Could someone explain how is this equal to that given in the notes I attached ?
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