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where A is arbitrary operator (not only ermiton), f is function, that < f | f > = 1. How to prove, that f is eigenfunction of operator A?
i've never used it before.dextercioby said:What do you know about this baby [itex] |f\rangle\langle f| [/itex]...?
Daniel.
Thank you. I've prooved it with your help. The puzzle is solveddextercioby said:[tex] \langle f|f\rangle =1 \Rightarrow |f\rangle\langle f|f\rangle =|f\rangle \Rightarrow |f\rangle\langle f|=\hat{1} [/tex]
Does that help...?
Daniel.
This equation is a mathematical representation of the relationship between a function f and an operator A. It states that the squared inner product of f with A f is equal to the inner product of f with the squared operator A^2 f.
This equation is commonly used in quantum mechanics to calculate the expectation value of a physical quantity, such as energy or momentum. It helps to determine the probability of a certain outcome for a given system.
The squared inner product represents the probability amplitude for a specific outcome. This means that the larger the squared inner product, the higher the probability of that outcome occurring.
Yes, this equation can be applied to any type of function and operator as long as they satisfy the necessary mathematical properties, such as being Hermitian and having a well-defined inner product.
Yes, this equation has been used in other fields of science, such as signal processing and image recognition, to analyze and process data. It can also be applied in engineering and economics for optimization problems.