Probability Density for Interferometer

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SUMMARY

The discussion centers on the challenges faced in calculating the probability density for an interferometer problem, specifically regarding the correct application of trigonometric identities and Euler's formula. The user highlights a critical error in the equation, noting the omission of a bracket that should include sin(delta). Despite attempts to simplify the equation using both manual calculations and scientific software, the user struggles to achieve the correct results and seeks guidance on the mathematical approach.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with Euler's formula
  • Basic knowledge of probability density functions
  • Experience with scientific computation tools
NEXT STEPS
  • Study the application of Euler's formula in quantum mechanics
  • Practice simplifying complex trigonometric expressions
  • Learn about probability density functions in quantum physics
  • Explore scientific computation tools like MATLAB or Python for symbolic mathematics
USEFUL FOR

Students and researchers in physics, particularly those focusing on quantum mechanics and interferometry, as well as anyone looking to enhance their mathematical skills in trigonometry and probability density calculations.

Einstein2nd
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Hey guys. All of the info for the problem is in a picture (sorry for not using the template).

I've tried working on this for ours and I still can't seem to get the trig identities right :(

http://img208.imageshack.us/img208/1770/assignmentquestion2.jpg

NOTE THAT THERE SHOULD BE ANOTHER BRACKET ON THE VERY END OF THE EQUATION FOR THE PROBABILITY DENSITY. IT SHOULD HAVE sin(delta)), NOT sin(delta) AS IT CURRENTLY HAS.

from that final step, I've done many things by both hand and scientific notebook and I just can't seem to get things to simplify down properly. There is no way I could possibly post all of the different things I've tried but don't worry, I'm not simply looking for a copy-paste answer into homework. I want to be able to understand the working.

Please clarify my initial working and steer me in the correct direction. I'm pretty sure that I understand the physics, it's just the maths...
 
Last edited by a moderator:
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Any chance of some help?

I was told to use Euler's formula (which I have tried in the past) and then separate the real and imaginary parts and then add the squares. I'm not getting the answer correct thoguh by doing this :(
 

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