On 11/5/2024 1:26 AM, Alan Grayson wrote:
On Tuesday, November 5, 2024 at 12:27:55 AM UTC-7 Russell Standish wrote:
On Mon, Nov 04, 2024 at 10:12:39PM -0800, Brent Meeker wrote:
>
>
>
> On 11/4/2024 9:47 PM, Alan Grayson wrote:
>
>
> On an unrelated issue, I recall your mention that wrt the S. Cat
thought
> experiment, there is no
> operator which has Alive and Dead as eigenvalues. IMO, this
implies that
> the S. Cat thought
> experiment just doesn't fit into any quantum thought experiment.
I then
> realized that the P
> operator for momentum must have a real value for its eigenvalues
since it's
> Hermitian, BUT
> how can a real value represent momentum, which is a vector? TY, AG
>
> The eigenvector would be momentum.
>
Sorry Brent - the measured momentum values are still eigenvalues.
Pick 3 orthogonal directions to measure the momentum, say x, y and z.
Then the momentum operators are -iℏ∂/∂x, -iℏ∂/∂y and -iℏ∂/∂z, and
the 3 eigenvalues are the 3 components of momentum.
One could also write it in vector form iℏ∇, in which case the
operator
has a vector-valued eigenvalue.
I don't think this is correct. Quantum operators are chosen to be
Hermitian, that is, self-adjoint IIRC, so that their eigenvalues will be
real. This is something that can be proven. So the question remains;
how can a real eigenvalue be a measured momentum, which
is a vector? AG
https://en.wikipedia.org/wiki/Momentum_operator
Brent
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