- #1
opeth_35
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Problem about boundries in this solve of quantum problem
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SUMMARY
The discussion centers on the boundaries of integrals in quantum mechanics, specifically in spherical coordinates. The integral limits are defined as r from 0 to ∞, θ from 0 to π, and φ from 0 to 2π. A clarification is provided regarding terminology, noting that "limit" or "bound" refers to numerical values, while "boundary" pertains to curves or surfaces. Additionally, a standard trigonometric identity, sin²θ = (1 - cos²θ)/2, is mentioned as potentially relevant to the problem.
PREREQUISITES- Understanding of spherical coordinates in calculus
- Familiarity with integrals in quantum mechanics
- Knowledge of trigonometric identities
- Basic concepts of limits and boundaries in mathematical contexts
- Research the application of spherical coordinates in quantum mechanics
- Study the derivation and application of trigonometric identities
- Explore integral calculus techniques for multi-variable functions
- Learn about boundary conditions in quantum mechanics problems
Students and professionals in physics, particularly those studying quantum mechanics, as well as mathematicians focusing on calculus and integral applications.
- #2
tiny-tim
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hey opeth_35! 
(btw, we say "limit" or "bound" for a number … "boundary" is for a curve or a surface
)
the integral is over the whole of space, and it's in spherical coordinates,
so the limits are: r from 0 to ∞, θ from 0 to π, and φ from 0 to 2π
(i don't understand your second question, but maybe the answer is that they used one of the standard trigonometric identities … sin2θ = (1 - cos2θ)/2)
(btw, we say "limit" or "bound" for a number … "boundary" is for a curve or a surface
)the integral is over the whole of space, and it's in spherical coordinates,
so the limits are: r from 0 to ∞, θ from 0 to π, and φ from 0 to 2π
(i don't understand your second question, but maybe the answer is that they used one of the standard trigonometric identities … sin2θ = (1 - cos2θ)/2)
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