Quantum operator methods – QM (quantum mouse) version
p. 1
SETUP:
Consider a quantum object (a "quantum lab mouse") and some new properties we can
measure. E.g., suppose "quantum weight",
W
, is a hermitian operator.
The corresponding physical measurement is "put the mouse on a quantum scale".
Interestingly, this scale reads either 1 (skinny mice) or 10 (heavy ones), but nothing else (!)
W
>
= 
> , W > = 10 >
.
(Because I'm no artist, I will simplify the icons for skinny and heavy mice to
and
respectively)
Note! Being skinny or heavy is
normal.
In fact, let us assume it is
ortho
normal (and complete)
Stare at these two eigenequations and make sure you, and your group, understand the notation:
which symbols are the eigenvectors here, what are the eigenvalues, in those equations?
What can you say about, e.g.
? (Explain)
"Quantum happiness",
H
, is also Hermitian. The corresponding physical measurement is "look at
the mouse's expression", yielding either a smile (happiness = +1), or frown (happiness = 1)

> =  > ,
but

> =  >
H
H
Note! Being happy or sad is
normal
. (Again, orthonormal, and complete)
Again, make sure you follow this notation:
what are the possible outcomes of a measurement of H?
Which symbols are the eigenvectors here, what are the eigenvalues?
(Note that "H" in this Tutorial has nothing to do with a Hamiltonian, sorry for the common letter)