- #1
Reshma
- 749
- 6
This is from a QM problem. A & B are the unknowns, k and K are given and [itex]i = \sqrt{-1}[/itex]. Use Cramer's rule to find A and show that |A|2 = 1.
[tex]A - B = -1[/tex]
[tex]ikA - KB = ik[/tex]
I applied Cramer's rule to determine A:
[tex]A = \frac{\left |\begin{array}{cc} -1 & -1 \\ ik & -K \end{array}\right|}{\left |\begin{array}{cc} 1 & -1 \\ ik & -K \end{array}\right|}[/tex]
So, I am left with:
[tex]A = \frac{K + ik}{-K + ik}[/tex]
I am stuck here, because this nowhere resembles the result I want to prove. Just guide me...
[tex]A - B = -1[/tex]
[tex]ikA - KB = ik[/tex]
I applied Cramer's rule to determine A:
[tex]A = \frac{\left |\begin{array}{cc} -1 & -1 \\ ik & -K \end{array}\right|}{\left |\begin{array}{cc} 1 & -1 \\ ik & -K \end{array}\right|}[/tex]
So, I am left with:
[tex]A = \frac{K + ik}{-K + ik}[/tex]
I am stuck here, because this nowhere resembles the result I want to prove. Just guide me...