Lysario – by Panagiotis Chatzichrisafis
"ούτω γάρ ειδέναι το σύνθετον υπολαμβάνομεν, όταν ειδώμεν εκ τίνων και πόσων εστίν …"
Archive for Januar, 2009
Liboff: “Introductory Quantum Mechanics”, 2nd edition p.86 exercise 3.16
Author: Panagiotis2 Jan
The exercise [1, p. 86 ex. 3.16] asks to prove that if the eigenfunctions and eigenvalues of an operator 
are 
and 
, respectively (
) then the eigenfunctions of a function 
having an expansion of the form:
will also be
with corresponding eigenvalues 
, 
. That is 
.
read the conclusion >
are and , respectively () then the eigenfunctions of a function having an expansion of the form:
 | (1) | ||
will also be
with corresponding eigenvalues , . That is .
read the conclusion >
Steven M. Kay: “Modern Spectral Estimation – Theory and Applications”, p. 14 exercise 1.1
Author: Panagiotis2 Jan
Exercise [1, p. 14 exercise 1.1] asks to prove that
is a monotonically increasing function over the interval
. Furthermore it asks to show that due to the monotonicity of the peaks of the spectral estimate shown in [1, Figure 1.2b] that they must also be present in the spectral estimate of [1, Figure 1.2a].
read the conclusion >
 | (1) | ||
is a monotonically increasing function over the interval
. Furthermore it asks to show that due to the monotonicity of the peaks of the spectral estimate shown in [1, Figure 1.2b] that they must also be present in the spectral estimate of [1, Figure 1.2a].
read the conclusion >