Does this equality have a name?

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In summary, the conversation discusses the equality known as the parallelogram law in quantum mechanics, which states that the sum of the squares of two wave functions in Hilbert's space is equal to twice the product of their norms plus twice the inner product of the two functions. This law holds true in basic linear algebra and has a geometric interpretation. Its significance in QM is that it can be used to define an inner product using the norm, and it is often seen in QM notebooks.
  • #1
M. next
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Hey there,

I was wondering if this equality in QM has a name or not.

It goes as follows:

llψ+øll^2 + llψ-øll^2 = 2llψll^2 + 2lløll^2

where: ψ and ø are wave functions in Hilbert's space.

If it doesn't specifically have a name, what is its significance in QM?

Thankis
 
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  • #2
It's just the parallelogram law. It has the usual geometric meaning and moreover if a norm satisfies it then the polarization identity can be used to define an inner product using the norm. The converse of course is trivial. This has nothing to do with QM it's just basic linear algebra.
 
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  • #3
Oh, okay. I see! The reason, I said QM, is because I saw it in QM notebook. Thanks!
 

FAQ: Does this equality have a name?

What is the purpose of naming an equality?

The purpose of naming an equality is to provide a concise and clear way to refer to a specific mathematical or logical statement or concept. This can make it easier to communicate and work with equations or ideas in various fields of study.

How are equalities typically named?

Equalities are typically named after the individuals who discovered or developed them, or after a characteristic or property that they possess. For example, the Pythagorean Theorem is named after the Greek mathematician Pythagoras, and the Associative Property is named after the property of grouping numbers in different ways without changing the result.

Are there any well-known equalities without names?

Yes, there are many well-known equalities that do not have specific names. Some may be referred to by multiple names or simply described by their properties, while others may not have been formally named yet.

Do all equalities need to be named?

No, not all equalities need to be named. Naming an equality is not a requirement, but it can be useful in certain contexts, such as in academic or research settings, to have a specific term to refer to a particular equality.

Can equalities have multiple names?

Yes, equalities can have multiple names. This can occur when different mathematicians or scientists have independently discovered the same equality and given it different names, or when an equality is known by different names in different fields of study.

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