Recent content by Mandragonia

I have finally found a satisfactory solution to the problem that I posed in this thread ! Careful examination of the boundary terms that arise at r=0 indicates that the problem of non-self-adjointness of the kinetic energy operator T is associated with the presence of odd powers of r in the...

The key point of this thread is that the operator ##T^2## is not to be trusted, since it can lead to unphysical results, such as a negative variance. The right representation is apparently with two operators ##T##, working on the left and right wavefunction ##\psi## respectively. Now in that...

Yet there is no guarantee that if you start a new thread in the QM forum on this subject, you will get any meaningful answers. The purpose of Physics Forums is to promote interesting and helpful discussions, but in reality these are scarce and occur only within the inner circle of experts.

Can the normalized radial distribution function Rho(r) be applied, as if it were a classical statistical distribution? For example: 1. Multiply Rho(r) by an arbitrary function of r, say f(r), and integrate from 0 to inf to obtain the average < f >. 2. Derive a cumulative probability P(t) by...

It stays the same for a free electron. Of course in a different setting it may increase too. I forgot to mention that the technical term for the gradual spreading of the wave packet is dispersion.

Atomic clocks...? Perhaps you can rotate them like a rod and fit them through the doors of perception. Peace man!

1. Is it just coincidence? Yes, I think so. The main focus of Erwin Schroedinger and his colleagues was on building a model that describes the atomic structure and its properties, in particular emission and absorption spectra. The behaviour of free electrons was (presumably) less important...

Yes! It is a entirely wrong way of looking at things. Time exists! At the cosmological level, at the human level, at the quantum level. Processes may indeed occur sequentially (that is the ordering aspect of time, to which you correctly refer), but they also occur at a certain rate. In quantum...

Radioactive decay of nuclei is a QM process. The decay rate is perfectly observable. This suggests to me that there are dynamic processes going on inside an unstable nucleus which effectively serve as an internal "clock".

You are welcome. And you are right. From the Maxwell equations (which are first order differential equations) one can derive the EM wave equation (which is a second order differential equation). The Schroedinger equation is a first order differential equation in time. At that time, everything...

Multiply the wave function Psi(r) by its complex conjugate and by spherical shell 4*pi*r^2 and you get the probability density Rho(r). The latter has a straightforward physical meaning. It tells you that at any moment in time the electron has a probability given by Rho(r)*dr to be at a distance...

There is also a historical reason why QM became developed in this direction. Early in the twentieth century it became apparent that electrons behave more like waves than like particles. Their behaviour is not well described by classical mechanics. Thus there was a need among physicists to...

Strangerep -- I acknowledge that one has to be careful when doing calculations on the hydrogen orbital; because it is ill-defined at r=0. I think Dauto has formulated it well: The equation I derived for the probability density of the kinetic energy is certainly not immune to this problem...

Right. Consider chess. It is a game played on a discrete 8*8 board, with discrete time element (the move), and with clearly defined pieces. This allows one to record the moves of a grandmaster game with 100 % accuracy. It looks something like: Anand-Carlsen, WK-match game 9, 2013. 1.d4 Nf6...

There is no evidence at all that we in live in 10 dimensions. Supersymmetry, superstrings, membranes etc are wonderful mathematical concepts, but totally detached from reality. In the mean time there are serious concerns in cosmology about inflation, dark matter, dark energy, vacuum energies...