please help , no idea about going through this integration :(?

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Mr.A

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im a undersraduate chemist had this problem in a past paper
Evaluate , ∫ Q.Q*dx where Q=√(30/L) .(L-x) and Q* is the complex conjugate of Q

(multiplication between Q and Q*)
(multiplication between √(30/L) and (L-x)


I know that when a complex number is multiplid by its complex conjugate it becomes a real number.. but the problem is, i dont see any complex number here..
and i think that we have to do some calculation first between the Q and Q*
what is the need of a complex conjugate at the absence of a complex number? and Ill be much grateful if you can explain all the steps as well :)
 
Last edited:
Mr.A said:
im a undersraduate chemist had this problem in a past paper
Evaluate , ∫ Q.Q*dx where Q=√(30/L) .(L-x) and Q* is the complex conjugate of Q

(multiplication between Q and Q*)
(multiplication between √(30/L) and (L-x)


I know that when a complex number is multiplid by its complex conjugate it becomes a real number.. but the problem is, i dont see any complex number here..
and i think that we have to do some calculation first between the Q and Q*
what is the need of a complex conjugate at the absence of a complex number? and Ill be much grateful if you can explain all the steps as well :)
Click to expand...

How do you define 'L'?
 
Mr.A said:
im a undersraduate chemist had this problem in a past paper
Evaluate , ∫ Q.Q*dx where Q=√(30/L) .(L-x) and Q* is the complex conjugate of Q

(multiplication between Q and Q*)
(multiplication between √(30/L) and (L-x)


I know that when a complex number is multiplid by its complex conjugate it becomes a real number.. but the problem is, i dont see any complex number here..
and i think that we have to do some calculation first between the Q and Q*
what is the need of a complex conjugate at the absence of a complex number? and Ill be much grateful if you can explain all the steps as well :)
Click to expand...
The quantity \(\displaystyle Q\cdot Q^*\) often arises when taking the amplitude of a wave function, which may be complex. A real number is equal to its conjugate.

If \(\displaystyle L\) is real, \(\displaystyle \displaystyle Q\cdot Q^* = |Q|^2 = \frac{30}{L}\ (L - x)^2\)

If \(\displaystyle L\) is complex, \(\displaystyle \displaystyle Q\cdot Q^* =\frac{30}{|L|}\ \left(|L|^2 + x^2 - 2\ \Re(L)\ x\right)\)

EDIT: I assumed you would be able to carry out the integration with respect to \(\displaystyle x\), if you were confident of the evaluation of the amplitude. Is that ok?
 
Last edited:
DrPhil said:
The quantity \(\displaystyle Q\cdot Q^*\) often arises when taking the amplitude of a wave function, which may be complex. A real number is equal to its conjugate.

If \(\displaystyle L\) is real, \(\displaystyle \displaystyle Q\cdot Q^* = |Q|^2 = \frac{30}{L}\ (L - x)^2\)

If \(\displaystyle L\) is complex, \(\displaystyle \displaystyle Q\cdot Q^* =\frac{30}{|L|}\ \left(|L|^2 + x^2 - 2\ \Re(L)\ x\right)\)

EDIT: I assumed you would be able to carry out the integration with respect to \(\displaystyle x\), if you were confident of the evaluation of the amplitude. Is that ok?
Click to expand...

THANK YOU SO MUCH Drphil :D yeah i can manage it now :)
 
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