A note on conventions
Is it ok to define kets in this way?
Some may object to the following syntax:
psi = ket ( exp(-x**2) )
Did we just loose some generality by imposing a coordinate representation on the ket? You may have seen the awkward notation sometimes used to caution against this:
The above expression seems to imply some relationship between kets in Hilbertspace and scalar functions on
Does the BraketLab-syntax erronously confine us to work in a coordinate representation by equating abstract vectors in Hilbert-space to functions in
Instead, the ket-class in Braketlab has to be instanciated from a suitable starting point, which in this case happens to be a function in coordinate space.
Note that there is a difference between the assignment operator =
common to most modern code-languages (like the Python-case above) and mathematical equality. The mathematical equivalent to the BraketLab syntax is more comparable to the following
where
Now, the following is true: a wavefunction
The ket
psi = ket ( exp(-p**2) )
,
and take p
to signify a momentum representation.
To state it explicitly: if the definition above holds, i.e.
then it does not seem so unreasonable to adopt the following convention:
where a ket is defined from its (in this case) coordinate representation.