Superposition of two wavefunctions

[Leb]

[SOLVED] Superposition of two wavefunctions

Homework Statement

The problem is more of complex number arithmetic more then conceptual :

Homework Equations

|\psi|^{2}=\psi\psi^{*}

The Attempt at a Solution

I simply used the equation given above, but instead of getting 2Re{...} I get :

|\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)

Could someone explain how is this equal to that given in the notes I attached ?

 

[spf]

Homework Statement

The problem is more of complex number arithmetic more then conceptual : View attachment 44717

Homework Equations

|\psi|^{2}=\psi\psi^{*}

The Attempt at a Solution

I simply used the equation given above, but instead of getting 2Re{...} I get :

|\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)

Could someone explaind how is this equal to that given in the notes I attached ?

The following link should be helpful:

http://en.wikipedia.org/wiki/Complex_number#Conjugation

 

[Leb]

Great, thanks !

 

[spf]

Great, thanks !

Glad to help.