Boundary terms in hilbert space goes vanish

In summary, Thant asked for a more exact reference to the common claim that square integrable functions must go to zero as the variable goes to infinity. The conversation also touched on the possibility that the function must also go to zero if certain operators are square integrable.
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notojosh
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Thant helped. thank you!
 
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  • #2
Can you give a more exact reference? A link to the exact page at google books would be the best way to reference it.

I assume it has something to do with the common claim that square integrable functions must go to zero as the variable goes to infinity ([itex]\psi(x)\rightarrow 0[/itex] when [itex]x\rightarrow\infty[/itex]), which is actually wrong. (There are counterexamples. See this thread). However, I think [itex]\psi(x)[/itex] must go to zero as x goes to infinity if [itex]Q\psi[/itex] (where Q is the position operator) is square integrable. Maybe it also has to go to zero if [itex]P\psi[/itex] (where P is the momentum operator) is square integrable? (I don't have time to think that through right now).
 
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1. What is the concept of boundary terms in Hilbert space?

Boundary terms in Hilbert space refer to the behavior of mathematical objects at the edges or boundaries of the space. In other words, these are the terms that arise when we consider the behavior of a mathematical function or operator at the boundary of a given space.

2. Why do boundary terms in Hilbert space go to zero?

Boundary terms in Hilbert space go to zero because of the boundary conditions imposed on the space. These conditions restrict the behavior of the mathematical objects at the edges of the space, resulting in the vanishing of the boundary terms.

3. How do boundary terms in Hilbert space affect calculations?

Boundary terms in Hilbert space can affect calculations by altering the values of certain mathematical objects, such as integrals or operators, at the boundaries of the space. This can lead to changes in the overall behavior of these objects and impact the results of calculations.

4. Can boundary terms in Hilbert space be ignored?

In most cases, boundary terms in Hilbert space can be ignored if the mathematical objects under consideration satisfy specific boundary conditions. However, in some cases, these terms may play a crucial role in calculations and cannot be ignored.

5. How do boundary terms in Hilbert space relate to physical systems?

Boundary terms in Hilbert space are closely related to physical systems as they represent the behavior of mathematical objects at the boundaries of these systems. In quantum mechanics, for example, these terms are used to describe the behavior of particles at the edges of a given system or in the presence of boundaries.

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