Problem about boundries in this solve of quantum problem

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In summary, the conversation is about a problem with boundaries in solving a quantum problem. The integral is over the whole of space in spherical coordinates with limits of r from 0 to ∞, θ from 0 to π, and φ from 0 to 2π. The second question is related to the use of a standard trigonometric identity, specifically sin2θ = (1 - cos2θ)/2.
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opeth_35
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hey

There is a problem about boundries in this solve of quantum problem. And I don't understand the boundries come from where on the integral.. I can not see it :( You will see in the picture... but If u want to see the other part of solve in problem I will add..
 

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hey opeth_35! :smile:

(btw, we say "limit" or "bound" for a number … "boundary" is for a curve or a surface :wink:)

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)
 

1. What is the significance of boundaries in quantum problems?

Boundaries play a crucial role in quantum problems as they can affect the behavior and properties of quantum systems. In quantum mechanics, a boundary can act as a potential barrier or well, influencing the energy levels and wave functions of particles within the system.

2. How do boundaries affect the solutions of quantum problems?

Boundaries can limit the possible solutions of a quantum problem. This is because the wave function of a particle must satisfy certain boundary conditions at the boundaries of the system. These boundary conditions determine the allowed energy levels and the behavior of the particle within the system.

3. Can the choice of boundaries affect the accuracy of quantum problem solutions?

Yes, the choice of boundaries can significantly impact the accuracy of solutions in quantum problems. Improperly chosen boundaries can lead to incorrect or invalid solutions. It is essential to carefully consider the boundaries when solving quantum problems to ensure accurate results.

4. How do scientists determine the appropriate boundaries for a quantum problem?

Determining the appropriate boundaries for a quantum problem is a highly complex and specialized process. Scientists use mathematical models and computational methods to analyze the system and determine the appropriate boundary conditions that will yield accurate solutions.

5. What challenges do boundaries pose in solving quantum problems?

Boundaries can present significant challenges in solving quantum problems due to their complex nature and the need for precise boundary conditions. In some cases, the boundaries may also interact with the particles in the system, making it more difficult to accurately predict the behavior of the system. Additionally, the presence of boundaries can also lead to the phenomenon of quantum tunneling, which further complicates the problem.

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