Recent content by Spin One

Oh ok, thanks! I see now how my intuition was wrong, since taking the δ function in the sense of a limit of a proper function, the derivative must be 0 at δ(0), +∞ at δ(-ε) and -∞ at δ(+ε). In that case, will the representation of d/dq be a "matrix" (of the generalized kind) with only two...

When considering the position representation of a system with one degree of freedom endowed with canonical co-ordinates and momenta q and p, Dirac deduces that: which is the representation of d/dq in "matrix" form. But the derivative of a delta function is, I assume (from the definition of the...

So dλ is introduced to make the product between each eigenket and dλ finite, since the eigenkets will be of "infinite length" in the sense of lim.Δλ→0[1/Δλ]. That makes sense. In that case, will the coefficients <λIΨ> be infinitesimal? Otherwise the integral would diverge, even over a finite range.

When one wants to represent a general ket in a basis consisting of eigenkets each attributed to an eigenvalue in a range, say from a to b, why does one take the integral of said kets from a to b w.r.t. the eigenvalues? I understand that the integral here plays a role analogous to a sum in the...