- #36
David Olivier
DrDu said:When you consider a free particle in an initial wavefunction ##\sim \exp(-bx^2)##
I was just giving an upper bound on the absolute value of the function; not saying it had to be a Gaussian!
DrDu said:When you consider a free particle in an initial wavefunction ##\sim \exp(-bx^2)##
David Olivier said:Thanks. I was not really trying to impose restrictions to ensure physicality; rather just trying to get things to work mathematically; and in particular ensure that the operators map the set to itself. I'm not sure my solution works, though; the "Hilbert space" I described may not be complete.
Physics Footnotes said:Again, if you like sorting out these kinds of subtleties, I think you'd enjoy von Neumann's book.
Physics Footnotes said:Also, keep in mind that domains always matter when an operator is unbounded, since no such operator can be defined on the entire Hilbert Space, while remaining self-adjoint.
Again, if you like sorting out these kinds of subtleties, I think you'd enjoy von Neumann's book.
Physics Footnotes said:Von Neumann (judged by most peers to be the best mathematician in the world at the time) tried, but was unable, to make coherent sense of Dirac's formalism (in particular, his reliance on a notoriously self-contradictory Delta Function)