# What is the Modulus of an Eigenvalue?

1. May 18, 2006

### dimensionless

2. May 18, 2006

### LeonhardEuler

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 $\sqrt{a^2+b^2}$.

3. May 19, 2006

Staff Emeritus
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.

4. May 19, 2006

### masudr

I'd credit the arrows to Argand, not Feynman...

5. May 19, 2006

Staff Emeritus
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.

6. May 25, 2006

### vroom

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