- #1
kasse
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Homework Statement
What does it take for
exp(ikL) - exp(-ikL) = 0
?
The Attempt at a Solution
cos(kL) + i sin(kL) - cos(kL) - i sin(kL) = 0
0 = 0
This suggests that kL can be anything, but this is not the right answer.
You are using exp(ikL)= cos(kl)+ i sin(kL), right?kasse said:Homework Statement
What does it take for
exp(ikL) - exp(-ikL) = 0
?
The Attempt at a Solution
cos(kL) + i sin(kL) - cos(kL) - i sin(kL) = 0
0 = 0
This suggests that kL can be anything, but this is not the right answer.
The equation above should be:kasse said:Homework Statement
What does it take for
exp(ikL) - exp(-ikL) = 0
?
The Attempt at a Solution
cos(kL) + i sin(kL) - cos(kL) - i sin(kL) = 0
kasse said:0 = 0
This suggests that kL can be anything, but this is not the right answer.
This equation represents the difference between the exponential functions of ikL and -ikL being equal to zero. It is commonly used in physics and mathematics to solve for values of kL.
This equation has various applications in different fields such as quantum mechanics, electromagnetic theory, and Fourier series. Solving it can help us understand physical phenomena and make accurate predictions.
The solutions to this equation depend on the value of kL. For kL = 0, the equation has no solution. For nonzero values of kL, the solutions are infinite and can be expressed as kL = 2nπ, where n is any integer.
To solve this equation, we can use algebraic manipulation and trigonometric identities. We can also use computer programs or calculators to find numerical solutions for specific values of kL.
This equation is used in many fields, including electrical engineering, signal processing, and quantum mechanics. It is essential in understanding the behavior of waves, resonance phenomena, and energy transfer in various systems.