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LCSphysicist
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How to perform a integral in momentum space
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SUMMARY
The discussion focuses on performing integrals in momentum space, specifically addressing the transition between two lines in an integral expression. The integral in question is $$\frac{4 \pi}{(2 \pi)^3} \int _{0} ^{\infty} p^2 e^{ip*r}/(2 E_p)$$. A key point raised is the role of the ##\cos(\theta)## term in the dot product, which influences the integration over ##d(\cos(\theta))## and alters the exponential components. Understanding these nuances is crucial for accurate calculations in quantum mechanics.
PREREQUISITES- Familiarity with quantum mechanics concepts, particularly momentum space integrals.
- Understanding of spherical coordinates and their application in integrals.
- Knowledge of exponential functions and their properties in complex analysis.
- Basic grasp of dot products and their significance in physics.
- Study the derivation of integrals in momentum space in quantum mechanics.
- Learn about the role of spherical coordinates in multi-dimensional integrals.
- Explore the properties of exponential functions in quantum field theory.
- Investigate the implications of dot products in physical calculations.
Physicists, particularly those specializing in quantum mechanics and quantum field theory, as well as students seeking to deepen their understanding of integrals in momentum space.
- #2
Frabjous
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There is a ##\cos(\theta)## in the dot product which brings out the ipr and causes the difference in the exponentials when you integrate over ##d(\cos(\theta))##
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