Hello!
"EIGENVALUES CALCULATION"
PROBLEM: Obtain the eigenvalues of the "A" matrix
If "lambda" is an eigenvalue, the determinant must be equal to zero
We expand
We substitute
We have the matrix
Now we write the determinant
We impose the condition that the determinant must be equal to zero
We obtain a second grade equation
We expand it
It is easy to solve
The solution is standard
We write the two eigenvalues
"lambda" must be equal to 11 or 4
We need the Hilbert space to explain the spin which is a pure quantum mechanical quantity
The spin is a pure quantum mechanical quantity
The spin has two different discrete values as a measurement result
The possible results are strongly discretized
The only way to put together the spin and the "X" operator is defining a Hilbert space
Why the "X" operator spectrum is continuos and the spin operator spectrum is discrete? ... Nobody knows
We need to define a common space for the spin and the Schrodinger wave function
Such a common space will be the Hilbert space
The old Schrodinger equation must be written in the Hilbert space to have a common framework with the spin
