What is the Modulus of an Eigenvalue?

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The modulus of an eigenvalue refers to its absolute value, which is particularly relevant in quantum mechanics where eigenvalues are often real due to their representation by Hermitian operators. In the case of complex eigenvalues, the modulus is calculated using the formula √(a² + b²), representing the length of the complex number as a vector in the plane. The discussion highlights the connection between complex amplitudes in quantum mechanics and their geometric interpretation, though some participants find the question trivial within the context of quantum mechanics. The conversation also touches on the historical attribution of the concept of complex numbers to Argand rather than Feynman. Overall, understanding the modulus of eigenvalues is crucial for interpreting their significance in quantum mechanics.
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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 \sqrt{a^2+b^2}.
 
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.
 
I'd credit the arrows to Argand, not Feynman...
 
masudr said:
I'd credit the arrows to Argand, not Feynman...

Absolutely!:approve: 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.
 
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
 

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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