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What is the Modulus of an Eigenvalue?
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LeonhardEuler
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The modulus of a real number is its absolute value. Since this is posted under quantum mechanics, I am assuming the the eigenvalue is real. In a more general case, though, the modulus of a complex number, a + bi, is [itex]\sqrt{a^2+b^2}[/itex].
selfAdjoint
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Yes, if you regard a complex number as a vector in the plane (Feynmann;s "little arrows") then its modulus is its length. This obviously agrees with LeonhardEuler's algebraic definition.
masudr
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I'd credit the arrows to Argand, not Feynman...
selfAdjoint
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masudr said:
Absolutely!
I wasn't giving him credit for the idea, but in his little book QED he refers to the complex amplitudes on his paths as little arrows. I always thought that was both sharp and funny.
vroom
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If u r talking of QM. Then this question appears meaningless to me.
In QM, every observable has got a hermitian operator representation. By the mathematics of hemitians we know they always have real eigenvalues.
so a mod amounts to change of sign if the eigval is -ve
In QM, every observable has got a hermitian operator representation. By the mathematics of hemitians we know they always have real eigenvalues.
so a mod amounts to change of sign if the eigval is -ve