Applications of Functional Analysis ?

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Functional analysis is closely related to physics, particularly in the field of Quantum Mechanics (QM). It provides a mathematical framework for understanding concepts such as unbounded operators, which are crucial in QM. The discussion highlights that functional analysis can help in solving quantum systems and understanding their properties. Many applications in physics stem from the theoretical foundations laid by functional analysis. Overall, the relationship between functional analysis and physics is significant, especially in advancing quantum theories.
azari123
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Hi guys,

I am new to the forum.

I have done a bit of reading on functional analysis lately.So I was wondering whether Functional Analysis can be related to physics in any way and what are the applications of that in physics?
 
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I've been reading about it lately too, and I believe that it has a number of applications in Quantum Mechanics. The last chapter of the book I'm reading on it is all about its applications in QM. Specifically the topic of Unbounded Operators is important (I haven't personally made it that far into the textbook, this is simply what I have gathered from the author's statements in the opening to the chapter and the book's preface).
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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